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Simplifying 10p2 + 50p + -16 = 0 Reorder the terms: -16 + 50p + 10p2 = 0 Solving -16 + 50p + 10p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 25p + 5p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 25p + 5p2)' equal to zero and attempt to solve: Simplifying -8 + 25p + 5p2 = 0 Solving -8 + 25p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 5p + p2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 5p + 1.6 + p2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 5p + p2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 5p + p2 = 0 + 1.6 5p + p2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 5p + p2 = 1.6 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 = 1.6 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 1.6 + 6.25 Combine like terms: 1.6 + 6.25 = 7.85 6.25 + 5p + p2 = 7.85 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 7.85 Calculate the square root of the right side: 2.801785145 Break this problem into two subproblems by setting (p + 2.5) equal to 2.801785145 and -2.801785145.Subproblem 1
p + 2.5 = 2.801785145 Simplifying p + 2.5 = 2.801785145 Reorder the terms: 2.5 + p = 2.801785145 Solving 2.5 + p = 2.801785145 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 = 2.801785145 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 2.801785145 + -2.5 p = 2.801785145 + -2.5 Combine like terms: 2.801785145 + -2.5 = 0.301785145 p = 0.301785145 Simplifying p = 0.301785145Subproblem 2
p + 2.5 = -2.801785145 Simplifying p + 2.5 = -2.801785145 Reorder the terms: 2.5 + p = -2.801785145 Solving 2.5 + p = -2.801785145 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 = -2.801785145 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -2.801785145 + -2.5 p = -2.801785145 + -2.5 Combine like terms: -2.801785145 + -2.5 = -5.301785145 p = -5.301785145 Simplifying p = -5.301785145Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.301785145, -5.301785145}Solution
p = {0.301785145, -5.301785145}
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