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How would you solve: \(-2x^2 + 10x + 25\)

tertre  Apr 11, 2017
 #1
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What does the question ask for?

MathNerd(version2.0)  Apr 11, 2017
 #2
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Solve for x:
-2 x^2 + 10 x + 25 = 0

Divide both sides by -2:
x^2 - 5 x - 25/2 = 0

Add 25/2 to both sides:
x^2 - 5 x = 25/2

Add 25/4 to both sides:
x^2 - 5 x + 25/4 = 75/4

Write the left hand side as a square:
(x - 5/2)^2 = 75/4

Take the square root of both sides:
x - 5/2 = (5 sqrt(3))/2 or x - 5/2 = -(5 sqrt(3))/2

Add 5/2 to both sides:
x = 5/2 + (5 sqrt(3))/2 or x - 5/2 = -(5 sqrt(3))/2

Add 5/2 to both sides:
Answer: | x = 5/2 + (5 sqrt(3))/2      or           x = 5/2 - (5 sqrt(3))/2

Guest Apr 11, 2017

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