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Simplifying 100p + -4p2 = 64 Solving 100p + -4p2 = 64 Solving for variable 'p'. Reorder the terms: -64 + 100p + -4p2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 100p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + 25p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-16 + 25p + -1p2)' equal to zero and attempt to solve: Simplifying -16 + 25p + -1p2 = 0 Solving -16 + 25p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -25p + p2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -25p + -16 + p2 = 0 + -16 Reorder the terms: 16 + -16 + -25p + p2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -25p + p2 = 0 + -16 -25p + p2 = 0 + -16 Combine like terms: 0 + -16 = -16 -25p + p2 = -16 The p term is -25p. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25p + 156.25 + p2 = -16 + 156.25 Reorder the terms: 156.25 + -25p + p2 = -16 + 156.25 Combine like terms: -16 + 156.25 = 140.25 156.25 + -25p + p2 = 140.25 Factor a perfect square on the left side: (p + -12.5)(p + -12.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (p + -12.5) equal to 11.842719282 and -11.842719282.Subproblem 1
p + -12.5 = 11.842719282 Simplifying p + -12.5 = 11.842719282 Reorder the terms: -12.5 + p = 11.842719282 Solving -12.5 + p = 11.842719282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + p = 11.842719282 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + p = 11.842719282 + 12.5 p = 11.842719282 + 12.5 Combine like terms: 11.842719282 + 12.5 = 24.342719282 p = 24.342719282 Simplifying p = 24.342719282Subproblem 2
p + -12.5 = -11.842719282 Simplifying p + -12.5 = -11.842719282 Reorder the terms: -12.5 + p = -11.842719282 Solving -12.5 + p = -11.842719282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + p = -11.842719282 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + p = -11.842719282 + 12.5 p = -11.842719282 + 12.5 Combine like terms: -11.842719282 + 12.5 = 0.657280718 p = 0.657280718 Simplifying p = 0.657280718Solution
The solution to the problem is based on the solutions from the subproblems. p = {24.342719282, 0.657280718}Solution
p = {24.342719282, 0.657280718}
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