Question 1048056: Solve the equation by completing the square. (Enter your answers as a comma-separated list.)
10x2 + 10x + 5 = 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve the equation by completing the square. (Enter your answers as a comma-separated list.)
10x^2 + 10x + 5 = 0
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Divide thru by 5 to get:
2x^2 + 2x + 1 = 0
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2x^2 + 2x = -1
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Complete the square and maintain the equality::
2(x^2+x+?) = -1 + 2*?
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2(x^2 + x + (!/2)^2) = -1 + 2(1/2)^2
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Factor the left side ; Simplify the right side
2(x+(1/2))^2 = -1 + 1/2
2(x+(1/2)^2 = -1/2
(x+(1/2)^2 = -1/4
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Take the square root of both sides to get::
x+(1/2) = i/2 or x+(1/2) = -i/2
x = (-1+i)/2 or x = (-1-i)/2
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Cheers,
Stan H.
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