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Simplifying -21p2 + -27p + 15 = 0 Reorder the terms: 15 + -27p + -21p2 = 0 Solving 15 + -27p + -21p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -9p + -7p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -9p + -7p2)' equal to zero and attempt to solve: Simplifying 5 + -9p + -7p2 = 0 Solving 5 + -9p + -7p2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.7142857143 + 1.285714286p + p2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 1.285714286p + 0.7142857143 + p2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 1.285714286p + p2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 1.285714286p + p2 = 0 + 0.7142857143 1.285714286p + p2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 1.285714286p + p2 = 0.7142857143 The p term is 1.285714286p. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286p + 0.4132653063 + p2 = 0.7142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286p + p2 = 0.7142857143 + 0.4132653063 Combine like terms: 0.7142857143 + 0.4132653063 = 1.1275510206 0.4132653063 + 1.285714286p + p2 = 1.1275510206 Factor a perfect square on the left side: (p + 0.642857143)(p + 0.642857143) = 1.1275510206 Calculate the square root of the right side: 1.061862053 Break this problem into two subproblems by setting (p + 0.642857143) equal to 1.061862053 and -1.061862053.Subproblem 1
p + 0.642857143 = 1.061862053 Simplifying p + 0.642857143 = 1.061862053 Reorder the terms: 0.642857143 + p = 1.061862053 Solving 0.642857143 + p = 1.061862053 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + p = 1.061862053 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + p = 1.061862053 + -0.642857143 p = 1.061862053 + -0.642857143 Combine like terms: 1.061862053 + -0.642857143 = 0.41900491 p = 0.41900491 Simplifying p = 0.41900491Subproblem 2
p + 0.642857143 = -1.061862053 Simplifying p + 0.642857143 = -1.061862053 Reorder the terms: 0.642857143 + p = -1.061862053 Solving 0.642857143 + p = -1.061862053 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + p = -1.061862053 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + p = -1.061862053 + -0.642857143 p = -1.061862053 + -0.642857143 Combine like terms: -1.061862053 + -0.642857143 = -1.704719196 p = -1.704719196 Simplifying p = -1.704719196Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.41900491, -1.704719196}Solution
p = {0.41900491, -1.704719196}
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