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Simplifying -2p2 + 28p = -6 Reorder the terms: 28p + -2p2 = -6 Solving 28p + -2p2 = -6 Solving for variable 'p'. Reorder the terms: 6 + 28p + -2p2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 28p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 14p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 14p + -1p2)' equal to zero and attempt to solve: Simplifying 3 + 14p + -1p2 = 0 Solving 3 + 14p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -14p + p2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -14p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + -14p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -14p + p2 = 0 + 3 -14p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 -14p + p2 = 3 The p term is -14p. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14p + 49 + p2 = 3 + 49 Reorder the terms: 49 + -14p + p2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + -14p + p2 = 52 Factor a perfect square on the left side: (p + -7)(p + -7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (p + -7) equal to 7.211102551 and -7.211102551.Subproblem 1
p + -7 = 7.211102551 Simplifying p + -7 = 7.211102551 Reorder the terms: -7 + p = 7.211102551 Solving -7 + p = 7.211102551 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + p = 7.211102551 + 7 p = 7.211102551 + 7 Combine like terms: 7.211102551 + 7 = 14.211102551 p = 14.211102551 Simplifying p = 14.211102551Subproblem 2
p + -7 = -7.211102551 Simplifying p + -7 = -7.211102551 Reorder the terms: -7 + p = -7.211102551 Solving -7 + p = -7.211102551 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = -7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + p = -7.211102551 + 7 p = -7.211102551 + 7 Combine like terms: -7.211102551 + 7 = -0.211102551 p = -0.211102551 Simplifying p = -0.211102551Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.211102551, -0.211102551}Solution
p = {14.211102551, -0.211102551}
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