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Simplifying 4p2 + 16p + -23 = -9 Reorder the terms: -23 + 16p + 4p2 = -9 Solving -23 + 16p + 4p2 = -9 Solving for variable 'p'. Reorder the terms: -23 + 9 + 16p + 4p2 = -9 + 9 Combine like terms: -23 + 9 = -14 -14 + 16p + 4p2 = -9 + 9 Combine like terms: -9 + 9 = 0 -14 + 16p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 8p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 8p + 2p2)' equal to zero and attempt to solve: Simplifying -7 + 8p + 2p2 = 0 Solving -7 + 8p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 4p + p2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 4p + 3.5 + p2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 4p + p2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 4p + p2 = 0 + 3.5 4p + p2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 4p + p2 = 3.5 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 3.5 + 4 Reorder the terms: 4 + 4p + p2 = 3.5 + 4 Combine like terms: 3.5 + 4 = 7.5 4 + 4p + p2 = 7.5 Factor a perfect square on the left side: (p + 2)(p + 2) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (p + 2) equal to 2.738612788 and -2.738612788.Subproblem 1
p + 2 = 2.738612788 Simplifying p + 2 = 2.738612788 Reorder the terms: 2 + p = 2.738612788 Solving 2 + p = 2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.738612788 + -2 p = 2.738612788 + -2 Combine like terms: 2.738612788 + -2 = 0.738612788 p = 0.738612788 Simplifying p = 0.738612788Subproblem 2
p + 2 = -2.738612788 Simplifying p + 2 = -2.738612788 Reorder the terms: 2 + p = -2.738612788 Solving 2 + p = -2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.738612788 + -2 p = -2.738612788 + -2 Combine like terms: -2.738612788 + -2 = -4.738612788 p = -4.738612788 Simplifying p = -4.738612788Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.738612788, -4.738612788}Solution
p = {0.738612788, -4.738612788}
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