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Simplifying p2 + -16p + -52 = 0 Reorder the terms: -52 + -16p + p2 = 0 Solving -52 + -16p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -16p + 52 + p2 = 0 + 52 Reorder the terms: -52 + 52 + -16p + p2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -16p + p2 = 0 + 52 -16p + p2 = 0 + 52 Combine like terms: 0 + 52 = 52 -16p + p2 = 52 The p term is -16p. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16p + 64 + p2 = 52 + 64 Reorder the terms: 64 + -16p + p2 = 52 + 64 Combine like terms: 52 + 64 = 116 64 + -16p + p2 = 116 Factor a perfect square on the left side: (p + -8)(p + -8) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (p + -8) equal to 10.770329614 and -10.770329614.Subproblem 1
p + -8 = 10.770329614 Simplifying p + -8 = 10.770329614 Reorder the terms: -8 + p = 10.770329614 Solving -8 + p = 10.770329614 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = 10.770329614 + 8 Combine like terms: -8 + 8 = 0 0 + p = 10.770329614 + 8 p = 10.770329614 + 8 Combine like terms: 10.770329614 + 8 = 18.770329614 p = 18.770329614 Simplifying p = 18.770329614Subproblem 2
p + -8 = -10.770329614 Simplifying p + -8 = -10.770329614 Reorder the terms: -8 + p = -10.770329614 Solving -8 + p = -10.770329614 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = -10.770329614 + 8 Combine like terms: -8 + 8 = 0 0 + p = -10.770329614 + 8 p = -10.770329614 + 8 Combine like terms: -10.770329614 + 8 = -2.770329614 p = -2.770329614 Simplifying p = -2.770329614Solution
The solution to the problem is based on the solutions from the subproblems. p = {18.770329614, -2.770329614}
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