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Simplifying -2p2 + 4p + 86 = 0 Reorder the terms: 86 + 4p + -2p2 = 0 Solving 86 + 4p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(43 + 2p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + 2p + -1p2)' equal to zero and attempt to solve: Simplifying 43 + 2p + -1p2 = 0 Solving 43 + 2p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + -2p + p2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + -2p + 43 + p2 = 0 + 43 Reorder the terms: -43 + 43 + -2p + p2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -2p + p2 = 0 + 43 -2p + p2 = 0 + 43 Combine like terms: 0 + 43 = 43 -2p + p2 = 43 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 43 + 1 Reorder the terms: 1 + -2p + p2 = 43 + 1 Combine like terms: 43 + 1 = 44 1 + -2p + p2 = 44 Factor a perfect square on the left side: (p + -1)(p + -1) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (p + -1) equal to 6.633249581 and -6.633249581.Subproblem 1
p + -1 = 6.633249581 Simplifying p + -1 = 6.633249581 Reorder the terms: -1 + p = 6.633249581 Solving -1 + p = 6.633249581 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + p = 6.633249581 + 1 p = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 p = 7.633249581 Simplifying p = 7.633249581Subproblem 2
p + -1 = -6.633249581 Simplifying p + -1 = -6.633249581 Reorder the terms: -1 + p = -6.633249581 Solving -1 + p = -6.633249581 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + p = -6.633249581 + 1 p = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 p = -5.633249581 Simplifying p = -5.633249581Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.633249581, -5.633249581}Solution
p = {7.633249581, -5.633249581}
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