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Simplifying -15p2 + 7p + 9 = 0 Reorder the terms: 9 + 7p + -15p2 = 0 Solving 9 + 7p + -15p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.6 + -0.4666666667p + p2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.4666666667p + 0.6 + p2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.4666666667p + p2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.4666666667p + p2 = 0 + 0.6 -0.4666666667p + p2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.4666666667p + p2 = 0.6 The p term is -0.4666666667p. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667p + 0.05444444448 + p2 = 0.6 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667p + p2 = 0.6 + 0.05444444448 Combine like terms: 0.6 + 0.05444444448 = 0.65444444448 0.05444444448 + -0.4666666667p + p2 = 0.65444444448 Factor a perfect square on the left side: (p + -0.2333333334)(p + -0.2333333334) = 0.65444444448 Calculate the square root of the right side: 0.808977407 Break this problem into two subproblems by setting (p + -0.2333333334) equal to 0.808977407 and -0.808977407.Subproblem 1
p + -0.2333333334 = 0.808977407 Simplifying p + -0.2333333334 = 0.808977407 Reorder the terms: -0.2333333334 + p = 0.808977407 Solving -0.2333333334 + p = 0.808977407 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + p = 0.808977407 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + p = 0.808977407 + 0.2333333334 p = 0.808977407 + 0.2333333334 Combine like terms: 0.808977407 + 0.2333333334 = 1.0423107404 p = 1.0423107404 Simplifying p = 1.0423107404Subproblem 2
p + -0.2333333334 = -0.808977407 Simplifying p + -0.2333333334 = -0.808977407 Reorder the terms: -0.2333333334 + p = -0.808977407 Solving -0.2333333334 + p = -0.808977407 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + p = -0.808977407 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + p = -0.808977407 + 0.2333333334 p = -0.808977407 + 0.2333333334 Combine like terms: -0.808977407 + 0.2333333334 = -0.5756440736 p = -0.5756440736 Simplifying p = -0.5756440736Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.0423107404, -0.5756440736}
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