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Simplifying -4p2 + 80p = -148 Reorder the terms: 80p + -4p2 = -148 Solving 80p + -4p2 = -148 Solving for variable 'p'. Reorder the terms: 148 + 80p + -4p2 = -148 + 148 Combine like terms: -148 + 148 = 0 148 + 80p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(37 + 20p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(37 + 20p + -1p2)' equal to zero and attempt to solve: Simplifying 37 + 20p + -1p2 = 0 Solving 37 + 20p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -20p + p2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -20p + 37 + p2 = 0 + 37 Reorder the terms: -37 + 37 + -20p + p2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -20p + p2 = 0 + 37 -20p + p2 = 0 + 37 Combine like terms: 0 + 37 = 37 -20p + p2 = 37 The p term is -20p. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20p + 100 + p2 = 37 + 100 Reorder the terms: 100 + -20p + p2 = 37 + 100 Combine like terms: 37 + 100 = 137 100 + -20p + p2 = 137 Factor a perfect square on the left side: (p + -10)(p + -10) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (p + -10) equal to 11.704699911 and -11.704699911.Subproblem 1
p + -10 = 11.704699911 Simplifying p + -10 = 11.704699911 Reorder the terms: -10 + p = 11.704699911 Solving -10 + p = 11.704699911 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 11.704699911 + 10 Combine like terms: -10 + 10 = 0 0 + p = 11.704699911 + 10 p = 11.704699911 + 10 Combine like terms: 11.704699911 + 10 = 21.704699911 p = 21.704699911 Simplifying p = 21.704699911Subproblem 2
p + -10 = -11.704699911 Simplifying p + -10 = -11.704699911 Reorder the terms: -10 + p = -11.704699911 Solving -10 + p = -11.704699911 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = -11.704699911 + 10 Combine like terms: -10 + 10 = 0 0 + p = -11.704699911 + 10 p = -11.704699911 + 10 Combine like terms: -11.704699911 + 10 = -1.704699911 p = -1.704699911 Simplifying p = -1.704699911Solution
The solution to the problem is based on the solutions from the subproblems. p = {21.704699911, -1.704699911}Solution
p = {21.704699911, -1.704699911}
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