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Simplifying 0 = p2 + -7p + -15 Reorder the terms: 0 = -15 + -7p + p2 Solving 0 = -15 + -7p + p2 Solving for variable 'p'. Combine like terms: 0 + 15 = 15 15 + 7p + -1p2 = -15 + -7p + p2 + 15 + 7p + -1p2 Reorder the terms: 15 + 7p + -1p2 = -15 + 15 + -7p + 7p + p2 + -1p2 Combine like terms: -15 + 15 = 0 15 + 7p + -1p2 = 0 + -7p + 7p + p2 + -1p2 15 + 7p + -1p2 = -7p + 7p + p2 + -1p2 Combine like terms: -7p + 7p = 0 15 + 7p + -1p2 = 0 + p2 + -1p2 15 + 7p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 15 + 7p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -7p + p2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -7p + 15 + p2 = 0 + 15 Reorder the terms: -15 + 15 + -7p + p2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -7p + p2 = 0 + 15 -7p + p2 = 0 + 15 Combine like terms: 0 + 15 = 15 -7p + p2 = 15 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = 15 + 12.25 Reorder the terms: 12.25 + -7p + p2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + -7p + p2 = 27.25 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (p + -3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
p + -3.5 = 5.220153254 Simplifying p + -3.5 = 5.220153254 Reorder the terms: -3.5 + p = 5.220153254 Solving -3.5 + p = 5.220153254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 5.220153254 + 3.5 p = 5.220153254 + 3.5 Combine like terms: 5.220153254 + 3.5 = 8.720153254 p = 8.720153254 Simplifying p = 8.720153254Subproblem 2
p + -3.5 = -5.220153254 Simplifying p + -3.5 = -5.220153254 Reorder the terms: -3.5 + p = -5.220153254 Solving -3.5 + p = -5.220153254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -5.220153254 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -5.220153254 + 3.5 p = -5.220153254 + 3.5 Combine like terms: -5.220153254 + 3.5 = -1.720153254 p = -1.720153254 Simplifying p = -1.720153254Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.720153254, -1.720153254}
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