SOLUTION: Solve the equation by completing the square: Solve the equation by completing the square: 4x^2-4x-9=0

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Question 801034: Solve the equation by completing the square: Solve the equation by completing the square: 4x^2-4x-9=0
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
complete the square:
4x^2 - 4x - 9 = 0
we want the coefficient of x^2 to be 1, divide eq by 4
x^2 - x - 9%2F4 = 0
x^2 - x + __ = 9%2F4
to complete the square, take half the coefficient of x, and square it
That's (1/2)^2 = 1/4, add to both sides
x^2 - x + 1%2F4 = 9%2F4 + 1%2F4
x^2 - x + 1%2F4 = 10%2F4
we can write it
{x - 1%2F2)^2 = 10%2F4
Find the square root of both sides
x - 1%2F2 = +/-sqrt%2810%2F4%29
x = 1%2F2 +/-sqrt%2810%2F4%29
extract the square root of 1/4
x = 1%2F2 +/-%281%2F2%29sqrt%2810%29
write the two solutions as
x = %281%2Bsqrt%2810%29%29%2F2
and
x = %281-sqrt%2810%29%29%2F2