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Simplifying p2 + -16p + -69 = -6 Reorder the terms: -69 + -16p + p2 = -6 Solving -69 + -16p + p2 = -6 Solving for variable 'p'. Reorder the terms: -69 + 6 + -16p + p2 = -6 + 6 Combine like terms: -69 + 6 = -63 -63 + -16p + p2 = -6 + 6 Combine like terms: -6 + 6 = 0 -63 + -16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -16p + 63 + p2 = 0 + 63 Reorder the terms: -63 + 63 + -16p + p2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -16p + p2 = 0 + 63 -16p + p2 = 0 + 63 Combine like terms: 0 + 63 = 63 -16p + p2 = 63 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 = 63 + 64 Reorder the terms: 64 + -16p + p2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + -16p + p2 = 127 Factor a perfect square on the left side: (p + -8)(p + -8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (p + -8) equal to 11.26942767 and -11.26942767.Subproblem 1
p + -8 = 11.26942767 Simplifying p + -8 = 11.26942767 Reorder the terms: -8 + p = 11.26942767 Solving -8 + p = 11.26942767 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 = 11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + p = 11.26942767 + 8 p = 11.26942767 + 8 Combine like terms: 11.26942767 + 8 = 19.26942767 p = 19.26942767 Simplifying p = 19.26942767Subproblem 2
p + -8 = -11.26942767 Simplifying p + -8 = -11.26942767 Reorder the terms: -8 + p = -11.26942767 Solving -8 + p = -11.26942767 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 = -11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + p = -11.26942767 + 8 p = -11.26942767 + 8 Combine like terms: -11.26942767 + 8 = -3.26942767 p = -3.26942767 Simplifying p = -3.26942767Solution
The solution to the problem is based on the solutions from the subproblems. p = {19.26942767, -3.26942767}
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