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Simplifying 0 = 6p2 + 96p + -384 Reorder the terms: 0 = -384 + 96p + 6p2 Solving 0 = -384 + 96p + 6p2 Solving for variable 'p'. Combine like terms: 0 + 384 = 384 384 + -96p + -6p2 = -384 + 96p + 6p2 + 384 + -96p + -6p2 Reorder the terms: 384 + -96p + -6p2 = -384 + 384 + 96p + -96p + 6p2 + -6p2 Combine like terms: -384 + 384 = 0 384 + -96p + -6p2 = 0 + 96p + -96p + 6p2 + -6p2 384 + -96p + -6p2 = 96p + -96p + 6p2 + -6p2 Combine like terms: 96p + -96p = 0 384 + -96p + -6p2 = 0 + 6p2 + -6p2 384 + -96p + -6p2 = 6p2 + -6p2 Combine like terms: 6p2 + -6p2 = 0 384 + -96p + -6p2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(64 + -16p + -1p2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(64 + -16p + -1p2)' equal to zero and attempt to solve: Simplifying 64 + -16p + -1p2 = 0 Solving 64 + -16p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 16p + p2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 16p + 64 + p2 = 0 + 64 Reorder the terms: -64 + 64 + 16p + p2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16p + p2 = 0 + 64 16p + p2 = 0 + 64 Combine like terms: 0 + 64 = 64 16p + p2 = 64 The p term is 16p. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16p + 64 + p2 = 64 + 64 Reorder the terms: 64 + 16p + p2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + 16p + p2 = 128 Factor a perfect square on the left side: (p + 8)(p + 8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (p + 8) equal to 11.313708499 and -11.313708499.Subproblem 1
p + 8 = 11.313708499 Simplifying p + 8 = 11.313708499 Reorder the terms: 8 + p = 11.313708499 Solving 8 + p = 11.313708499 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + p = 11.313708499 + -8 p = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 p = 3.313708499 Simplifying p = 3.313708499Subproblem 2
p + 8 = -11.313708499 Simplifying p + 8 = -11.313708499 Reorder the terms: 8 + p = -11.313708499 Solving 8 + p = -11.313708499 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + p = -11.313708499 + -8 p = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 p = -19.313708499 Simplifying p = -19.313708499Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.313708499, -19.313708499}Solution
p = {3.313708499, -19.313708499}
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