SOLUTION: Solve the equation 15p ^ 2 + 7p - 4 = 0 by completing the square.

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Question 210971: Solve the equation 15p ^ 2 + 7p - 4 = 0 by completing the square.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square:
15p%5E2%2B7p-4+=+0 Divide through by 15 to get the coefficient of p%5E2 equal to 1.
p%5E2%2B%287%2F15%29p-4%2F15+=+0 Now add 4%2F15 to both sides of the equation.
p%5E2%2B%287%2F15%29p+=+4%2F15 Complete the square in p by adding the square of half the p-coefficient to both sides. %28%281%2F2%29%287%2F15%29%29%5E2+=+49%2F900
p%5E2%2B%287%2F15%29p+%2B+49%2F900+=+%287%2F15%29%2B49%2F900 Factor the left side and simplify the right side.
%28p%2B7%2F30%29%5E2+=+%28420%2F900%29%2B%2849%2F900%29
%28p%2B%287%2F30%29%29%5E2+=+469%2F900 take the square root of both sides.
p%2B%287%2F30%29+=+sqrt%28469%29%2F30 or p%2B%287%2F30%29+=+-sqrt%28469%29%2F30Subtract %287%2F30%29 from both sides.
p+=+%28%28-7%2F30%29%2Bsqrt%28469%29%29%2F30 or p+=+%28%28-7%2F30%29-sqrt%28469%29%29%2F30
p+=+%28-7%2Bsqrt%28469%29%29%2F30 or p+=+%28-7-sqrt%28469%29%29%2F30