Question 622006: i am doing quadratic equation and i need help with how y'all do steps and explanation.
i have to find what a is and b
By completing the square, the expression x^2+16 x +28 equals (x+A)^2+B
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! To complete the square, follow these steps.
First you want to move the "loose" number to the other side of the equation:
x^2 + 16x + 28
x^2 + 16x = -28
Next, you want to take half of the x-term (that is, divide it by two) and square it. So in this case, take 16, divide it by 2 (8) and then square that (8^2=64). Add this square to both sides of the equation.
x^2 + 16x = -28
x^2 + 16x + 64 = -28 +64
x^2 + 16x + 64 = 36
Finally, convert the left-hand side to squared form. To find the value "A" of the squared form, take the square root of the "loose" number on the left side of the equation, in our case, 64 (sqrt(64) = +/-8). Be careful of the sign. To know whether it is +8 or -8, look at the middle x-term (16x). We need A + A = 16. So +8 is the answer.
x^2 + 16x + 64 = 36
(x + 8)^2 = 36
So your answer is (x+8)^2=36.
You can always check your work by factoring to make sure the sign is right:
(x+8)^2=36
(x+8)(x+8) = 36
x^2 + 8x + 8x + 64 = 36
x^2 + 16x + 64 = 36
x^2 + 16x = -28
x^2 + 16x + 28 (the original equation - so you know your answer is correct)
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