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Simplifying p2 + -12p + -52 = 0 Reorder the terms: -52 + -12p + p2 = 0 Solving -52 + -12p + 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 + -12p + 52 + p2 = 0 + 52 Reorder the terms: -52 + 52 + -12p + p2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -12p + p2 = 0 + 52 -12p + p2 = 0 + 52 Combine like terms: 0 + 52 = 52 -12p + p2 = 52 The p term is -12p. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12p + 36 + p2 = 52 + 36 Reorder the terms: 36 + -12p + p2 = 52 + 36 Combine like terms: 52 + 36 = 88 36 + -12p + p2 = 88 Factor a perfect square on the left side: (p + -6)(p + -6) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (p + -6) equal to 9.38083152 and -9.38083152.Subproblem 1
p + -6 = 9.38083152 Simplifying p + -6 = 9.38083152 Reorder the terms: -6 + p = 9.38083152 Solving -6 + p = 9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = 9.38083152 + 6 Combine like terms: -6 + 6 = 0 0 + p = 9.38083152 + 6 p = 9.38083152 + 6 Combine like terms: 9.38083152 + 6 = 15.38083152 p = 15.38083152 Simplifying p = 15.38083152Subproblem 2
p + -6 = -9.38083152 Simplifying p + -6 = -9.38083152 Reorder the terms: -6 + p = -9.38083152 Solving -6 + p = -9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = -9.38083152 + 6 Combine like terms: -6 + 6 = 0 0 + p = -9.38083152 + 6 p = -9.38083152 + 6 Combine like terms: -9.38083152 + 6 = -3.38083152 p = -3.38083152 Simplifying p = -3.38083152Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.38083152, -3.38083152}
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