SOLUTION: Determine the value or values of d that complete the square for the expression. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x^2 +

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine the value or values of d that complete the square for the expression. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x^2 +      Log On


   

Question 901511: Determine the value or values of d that complete the square for the expression. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
x^2 + dx + 64
and
x^2 + dx + 49/4
Found 3 solutions by Edwin McCravy, josgarithmetic, stanbon:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Set x%5E2+%2B+dx+%2B+64 equal to the square of the 
sum of the square roots of the first and third terms

x%5E2+%2B+dx+%2B+64=%28x%2B8%29%5E2

x%5E2%2Bdx%2B64=%28x%2B8%29%28x%2B8%29

x%5E2%2Bdx%2B64=x%5E2%2B16x%2B64

x²'s and 64s cancel

dx=16x

d=16

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x^2 + dx + 49/4

Set x%5E2+%2B+dx+%2B+49%2F4 equal to the square of the
sum of the square roots of the first and third terms

x%5E2+%2B+dx+%2B+49%2F4=%28x%2B7%2F2%29%5E2

x%5E2%2Bdx%2B49%2F4=%28x%2B7%2F2%29%28x%2B7%2F2%29

x%5E2%2Bdx%2B49%2F4=x%5E2%2B7x%2B49%2F4

x²'s and 49%2F4s cancel

dx=7x

d=7

Edwin

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A more typical lesson on Completing The Square is here:

http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev

You can use the main action for an expression or for an equation.

Your question takes an uncommon direction.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the value or values of d that complete the square for the expression. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
---------------------
Perfect-square Form:: (x+y)^2 = x^2 + 2xy + y^2
----
Notice::The 2nd term is the product of 2 times sqrt(1st term)*sqrt(last term)
x^2 + dx + 64
2nd term = 2(sqrt(x^2))(sqrt(64)) = 2x*8 = 16x
Ans: x^2 + 16x + 64
d = 16
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and
x^2 + dx + 49/4
2nd = 2(sqrt(x^2)*sqrt(49/4) = 2x*(7/2) = 7x
Ans: x^2 + 7x + (49/4)
d = 7
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Cheers,
Stan H.
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