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Simplifying 5p2 + 25p = 130 Reorder the terms: 25p + 5p2 = 130 Solving 25p + 5p2 = 130 Solving for variable 'p'. Reorder the terms: -130 + 25p + 5p2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 25p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-26 + 5p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-26 + 5p + p2)' equal to zero and attempt to solve: Simplifying -26 + 5p + p2 = 0 Solving -26 + 5p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 5p + 26 + p2 = 0 + 26 Reorder the terms: -26 + 26 + 5p + p2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 5p + p2 = 0 + 26 5p + p2 = 0 + 26 Combine like terms: 0 + 26 = 26 5p + p2 = 26 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 26 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 26 + 6.25 Combine like terms: 26 + 6.25 = 32.25 6.25 + 5p + p2 = 32.25 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (p + 2.5) equal to 5.678908346 and -5.678908346.Subproblem 1
p + 2.5 = 5.678908346 Simplifying p + 2.5 = 5.678908346 Reorder the terms: 2.5 + p = 5.678908346 Solving 2.5 + p = 5.678908346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 5.678908346 + -2.5 p = 5.678908346 + -2.5 Combine like terms: 5.678908346 + -2.5 = 3.178908346 p = 3.178908346 Simplifying p = 3.178908346Subproblem 2
p + 2.5 = -5.678908346 Simplifying p + 2.5 = -5.678908346 Reorder the terms: 2.5 + p = -5.678908346 Solving 2.5 + p = -5.678908346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -5.678908346 + -2.5 p = -5.678908346 + -2.5 Combine like terms: -5.678908346 + -2.5 = -8.178908346 p = -8.178908346 Simplifying p = -8.178908346Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.178908346, -8.178908346}Solution
p = {3.178908346, -8.178908346}
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