SOLUTION: Solve 2x*squared* - 5x=5 by completing the square.

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Question 140384: Solve 2x*squared* - 5x=5 by completing the square.
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 2x*squared* - 5x=5 by completing the square.
:
2x^2 - 5x + ___ = 5
:
Divide the equation by 2 to make the coefficient of x^2 = 1
x^2 - (5/2)x + ___ = 5/2
:
Divide 5/2 by 2 and square it to complete the square, add to both sides
x^2 - (5/2)x + 25/16 = 5/2 + 25/16
:
x^2 - (5/2)x + 25/16 = 40/16 + 25/16
:
x^2 - (5/2)x + 25/16 = 65/16
:
(x - 5%2F4)^2 = 65%2F16
:
x - 5%2F4 = +/-sqrt%2865%2F16%29
:
x - 5%2F4 = +/-%281%2F4%29sqrt%2865%29
:
x = 5%2F4 +/-%281%2F4%29sqrt%2865%29
You can write it:
x = %285+%2B+sqrt%2865%29%29%2F4
and
x = %285+-+sqrt%2865%29%29%2F4

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 2x*squared* - 5x=5 by completing the square.
2x^2 - 5x = 5
Factor out the "2":
2(x^2 -(5/2)x+? = 5 + 2*?
Complete the square on the x-terms:
2(x^2 -(5/2)x + (5/4)^2) = 5 + 2(5/4)^2
Simplify:
2(x-(5/4)^2 = 130/16
Divide both sides by 2, then take the square root of both sides to get:
(x-(5/4)) = +- sqrt(65/16)
Simplify:
x = (5/4) +- (1/4)sqrt(65)
x = (5 +-sqrt(65))/4
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Cheers,
Stan H.