Impress your Math Teacher! Solve by Completing The Square
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- เผยแพร่เมื่อ 17 เม.ย. 2023
- How to solve a quadratic equation by completing the square - step by step example.
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If I were to have to solve this equation I probably use the formula, but this is a good exercise in completing the square hand and understanding algebraic operations
Thank you for your in depth analysis of how to solve quadratic equation using completing the square methods.
THANK YOU in all languages of the world
greetings from Yemen
Thank you!❤😂
My answer I got from completing the square was ⇒x=(-5±√33)/4
I admit that completing the square is my weakest skill in dealing with quadratic equation solving.
My first step was dividing the equation by 2 to make the A coefficient 1 (ax²+bx+c=0). Then move the constant to the other side.
x²+5/2x=1/2 Let's make it 10/4 as the B coefficient and make it 16ths on the other side and then add 25/16 to both sides (perfect square).
x²+10/4x+25/16=8/16+25/16 factor the left and simplify the right
(x+5/4)²=33/16 find square root of each side (remembering it is ± on the right)
x+5/4=±√33/4. move the 5/4 to the other side and simplify
x=(-5±√33)/4
Let's try the quadratic formula to check this.
x=(-b±√b²-4ac)/2
x=-5±√(25-4(2)(-1)/2(2)
x=(-5±√33)/4
This checks. So that is the answer.
But this took me forever -- I would have preferred the quadratic formula as this would have been much faster.
ever since learning the quadratic equation I forgot other methods!
so I searched internet and relearned completing the square.
2X^2 + 5X - 1 = 0
2X^2 + 5X = 1
X^2 + (5/2)X = 1/2
X^2 + (5/2)X + (25/16) = (1/2) + (25/16)
(X + (5/4))^2 = ((8/16) + (25/16))
(X + (5/4)) = sqrt(33/16)
(X + 5/4) = +/- (1/4)(sqrt(33))
X = -(5/4) +/-(1/4)(sqrt(33))
= (1/4)(-5 +/-(sqrt(33))
= -(5/4) +/- sqrt (33/16)
VERIFY
I'll use the quadratic equation...
i.e. ( -b +/- sqrt (b^2 -4ac))/2a
a = 2
b = 5
c = -1
so....
(-5 +/- sqrt (5^2 -(4)(2)(-1))/ (2)(2)
(-5 +/- sqrt (25 + 8))/4
(-5 +/- sqrt (33))/4
(-5/4 +/- sqrt (33/16) ✔️✔️✔️
or -5/4 = -1.25
sqrt(33/16) = sqrt(2.062) = 1.436
-1.25 +/- 1.436
-1.25 + 1.436 = 0.186 root1
-1.25 - 1.436 = -2.686 root2
VERIFY
2X^2 + 5X - 1 = 0
root.1 X = 0.186
(2)(0.186)^2 + (5)(0.186) - 1 =? 0
0.069 + 0.93 - 1 ?= 0
0.999 - 1 ?= 0 ✔️✔️✔️
root.2 X = -2.686
2X^2 + 5X - 1 = 0
(2)(-2.686)^2 + (5)(-2.686) - 1 ?= 0
14.429 - 13.43 - 1 ?= 0
0.999 - 1 ?= 0 ✔️✔️✔️
When you remove the square root of 33 over 4 why does the 4 not also become + and - too.
You turned the left side of the equation into a perfect trinomial square. That's how it's done.👍
Really helpful video! But the long intro was dragging on and on unnecesarily ;P
What an incredibly good teacher!!
Thank you so much John.
The perfect √square root is 4
Density
What you did here, is it actually to create the proof of the quadratic formula??
in the end its the quadratic formula ! just long way
Technically the x² part doesn't need to be 1, any square number will do. I found the numbers much easier to deal with by doubling the original equation (2x² + 5x - 1 = 0) to get (4x² + 10x - 2 = 0) and proceeding the rest the same way. Meant I was dealing with numbers over 4 instead of numbers over 16.
But that’s not the completing the square method.
Also, you got a different equation. (2x^2 + 5X - 1 = 0) times 2 equals 4 X ^4 + 10X - 2 = 0. Now you have a quart Uc equation, instead of a quadratic equation.
@@andrewm6424 why does it become X to the power of 4? I just multiplied by two, and then completed the square.
@@andrewm6424you don’t double the power, so you have an error.
Logical
Lost me when he divided by 2!
This is the first time that the answer makes no sense regarding how it was arrived at by the teacher. The rule is that whatever you do to one side of the equation, you must do to the other. I have know idea how the 5/2X is converted to 5/4 by in essence,3 removing the X and multiplying by 2? That is a violation of basic math, the variable must be accounted for, yet in his explanation it is nonexistent. I got the first part easily: X squared + 5/2X = 1/2, but it goes into nonsense for me. I might need to "brush" up on basic algebra, but I'm a College graduate with a Degree in Biochemistry and Biology w/ emphasis on Integral Calculus. Please help, where have I gone wrong? Granted, I'm 67 and graduated in 1980. but still, this hurts!!
When its has lot of ,exponents ,roots in denominator,power : people has to know the properties 😅.
Insoluble.
I am going to go and drink some wobbly pops catch you tomorrow
How9/4?
The quadratic formula would have been faster but the CT was required
It is interesting that if you use the general form of ax^2 + bx + c =0 and complete the square process you end up with the quadratic formula!
I've been watching all the videos I can on quadratic equations and I can't understand it. Everyone who teaches this teaches it like you already know how to do it. No one really takes the time to explain it step for step and when they do they never explain why it is done that way. Why you do this step in this exact order. Why do we divide by two, why do we have to divide everything by 2 separately, things like that. Sadly after weeks of trying i don't think I'm ever going to figure this stuff out. Do you have any videos where you explain this stuff in greater detail?
If you need help maybe you need a one on one tutor, I know it's confusing if you don't have experience solving equations. I know I can help, if you're interested, please let me know.
I had to think about that also. It is best explained by squaring(x+b) and seeing the resulting coefficients. Then running it backwards you see why you take the 1/2 b and then square that for the perfect square.
One way that might help you, is to go the other direction. Start with the solution and end up with the equation. That way you can see where the equation comes from. Multiply (2x-4)(x-1). Set it all equal to zero.
☝🏻I would have enjoyed math more had the question AND answer then breakdown how you came to the conclusion...my brain seems to work backwards much like dyslexia but in its own recognition 🤷🏻♀️
💁🏻♀️My "struggle" would be (did i forget to mention my brain works in its own way and inaccurately🙄) :
2X × 1 = 2
2X × 2 = 4
2 + 4 = 6
6 - 5 = 1
Thanks for this. But, No explanation as to why you half the x coefficient. And square. Just like many demonstrations it glosses over the fundamentals of maths. Better to show this graphically and then show that the quadratic equation is derived from completing the square. Also no mention of the fact that you can use completing the square to find the turning point of the quadratic.
WTF!!
Too much ineffective talk.
gotta
(-1-) know the student
(-2-) pace delivery to accommodate the typical slow student
@@tomtke7351yeah but 17 minute video on doing one easy problem?
@@blugarr but he's teaching NOT entertaining... his classroom is directed at the unknowing.... the rest of us are reviewing. Did you know you can turn up playback speed by up to 2x?
Too long and complicated. Better to skip this and focus on other math tools.
@thomashawkinson7017. Agreed. But why does the quadratic formula work? 😃
Point being, if I learned this in school, I completely forgot it after because I was taught to memorize everything for a test. So once the test was over, I didn’t need it. In essence, this caused me to graduate without learning anything. This video is important because it helps show the process that explains the quadratic formula, which will help others remember that well because they will know why it is needed and works.
yeah i skipped it 18 years ago and now after all that time i am struggling coz it came back to me at uni lol
@@andrewm6424interesting how different minds think. I was never good at bulk memory work, but how the mechanism worked.
Example: citric acid cycle I viewed as a mechanism that if you interferes with part of the cycle what would be the outcome. Never anticipated that the exam would be “ draw the citric acid cycle”, no question on what would happen in a diseased state what would be the outcome. To this day I realize some people only regurgitate memorized knowledge, while others use knowledge to extrapolate or manipulate that knowledge. Good engineers are generally not rote memorization.
Waste of time. Use quadratic formula. Easy