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Simplifying -4p2 + -6p + 15 = 0 Reorder the terms: 15 + -6p + -4p2 = 0 Solving 15 + -6p + -4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + 1.5p + p2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 1.5p + 3.75 + p2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 1.5p + p2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 1.5p + p2 = 0 + 3.75 1.5p + p2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 1.5p + p2 = 3.75 The p term is 1.5p. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5p + 0.5625 + p2 = 3.75 + 0.5625 Reorder the terms: 0.5625 + 1.5p + p2 = 3.75 + 0.5625 Combine like terms: 3.75 + 0.5625 = 4.3125 0.5625 + 1.5p + p2 = 4.3125 Factor a perfect square on the left side: (p + 0.75)(p + 0.75) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (p + 0.75) equal to 2.076655966 and -2.076655966.Subproblem 1
p + 0.75 = 2.076655966 Simplifying p + 0.75 = 2.076655966 Reorder the terms: 0.75 + p = 2.076655966 Solving 0.75 + p = 2.076655966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = 2.076655966 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = 2.076655966 + -0.75 p = 2.076655966 + -0.75 Combine like terms: 2.076655966 + -0.75 = 1.326655966 p = 1.326655966 Simplifying p = 1.326655966Subproblem 2
p + 0.75 = -2.076655966 Simplifying p + 0.75 = -2.076655966 Reorder the terms: 0.75 + p = -2.076655966 Solving 0.75 + p = -2.076655966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = -2.076655966 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = -2.076655966 + -0.75 p = -2.076655966 + -0.75 Combine like terms: -2.076655966 + -0.75 = -2.826655966 p = -2.826655966 Simplifying p = -2.826655966Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.326655966, -2.826655966}
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