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Simplifying 14p2 + 140p = 126 Reorder the terms: 140p + 14p2 = 126 Solving 140p + 14p2 = 126 Solving for variable 'p'. Reorder the terms: -126 + 140p + 14p2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 140p + 14p2 = 0 Factor out the Greatest Common Factor (GCF), '14'. 14(-9 + 10p + p2) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-9 + 10p + p2)' equal to zero and attempt to solve: Simplifying -9 + 10p + p2 = 0 Solving -9 + 10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + 10p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10p + p2 = 0 + 9 10p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 10p + p2 = 9 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 9 + 25 Reorder the terms: 25 + 10p + p2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10p + p2 = 34 Factor a perfect square on the left side: (p + 5)(p + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (p + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
p + 5 = 5.830951895 Simplifying p + 5 = 5.830951895 Reorder the terms: 5 + p = 5.830951895 Solving 5 + p = 5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.830951895 + -5 p = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 p = 0.830951895 Simplifying p = 0.830951895Subproblem 2
p + 5 = -5.830951895 Simplifying p + 5 = -5.830951895 Reorder the terms: 5 + p = -5.830951895 Solving 5 + p = -5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.830951895 + -5 p = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 p = -10.830951895 Simplifying p = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.830951895, -10.830951895}Solution
p = {0.830951895, -10.830951895}
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