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Simplifying p2 + 16p + 18 = 4 Reorder the terms: 18 + 16p + p2 = 4 Solving 18 + 16p + p2 = 4 Solving for variable 'p'. Reorder the terms: 18 + -4 + 16p + p2 = 4 + -4 Combine like terms: 18 + -4 = 14 14 + 16p + p2 = 4 + -4 Combine like terms: 4 + -4 = 0 14 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 16p + -14 + p2 = 0 + -14 Reorder the terms: 14 + -14 + 16p + p2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 16p + p2 = 0 + -14 16p + p2 = 0 + -14 Combine like terms: 0 + -14 = -14 16p + p2 = -14 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 = -14 + 64 Reorder the terms: 64 + 16p + p2 = -14 + 64 Combine like terms: -14 + 64 = 50 64 + 16p + p2 = 50 Factor a perfect square on the left side: (p + 8)(p + 8) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (p + 8) equal to 7.071067812 and -7.071067812.Subproblem 1
p + 8 = 7.071067812 Simplifying p + 8 = 7.071067812 Reorder the terms: 8 + p = 7.071067812 Solving 8 + p = 7.071067812 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 = 7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + p = 7.071067812 + -8 p = 7.071067812 + -8 Combine like terms: 7.071067812 + -8 = -0.928932188 p = -0.928932188 Simplifying p = -0.928932188Subproblem 2
p + 8 = -7.071067812 Simplifying p + 8 = -7.071067812 Reorder the terms: 8 + p = -7.071067812 Solving 8 + p = -7.071067812 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 = -7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + p = -7.071067812 + -8 p = -7.071067812 + -8 Combine like terms: -7.071067812 + -8 = -15.071067812 p = -15.071067812 Simplifying p = -15.071067812Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.928932188, -15.071067812}
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