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Simplifying 4p2 + 4p + -6 = 0 Reorder the terms: -6 + 4p + 4p2 = 0 Solving -6 + 4p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 2p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 2p + 2p2)' equal to zero and attempt to solve: Simplifying -3 + 2p + 2p2 = 0 Solving -3 + 2p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p + p2 = 0 + 1.5 p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 p + p2 = 1.5 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + p2 = 1.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 1.25 + p2 = 1.75 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (p + 0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
p + 0.5 = 1.322875656 Simplifying p + 0.5 = 1.322875656 Reorder the terms: 0.5 + p = 1.322875656 Solving 0.5 + p = 1.322875656 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 1.322875656 + -0.5 p = 1.322875656 + -0.5 Combine like terms: 1.322875656 + -0.5 = 0.822875656 p = 0.822875656 Simplifying p = 0.822875656Subproblem 2
p + 0.5 = -1.322875656 Simplifying p + 0.5 = -1.322875656 Reorder the terms: 0.5 + p = -1.322875656 Solving 0.5 + p = -1.322875656 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -1.322875656 + -0.5 p = -1.322875656 + -0.5 Combine like terms: -1.322875656 + -0.5 = -1.822875656 p = -1.822875656 Simplifying p = -1.822875656Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.822875656, -1.822875656}Solution
p = {0.822875656, -1.822875656}
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