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Simplifying 8p2 + -4p = 20 Reorder the terms: -4p + 8p2 = 20 Solving -4p + 8p2 = 20 Solving for variable 'p'. Reorder the terms: -20 + -4p + 8p2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -4p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -1p + 2p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1p + 2p2)' equal to zero and attempt to solve: Simplifying -5 + -1p + 2p2 = 0 Solving -5 + -1p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -0.5p + p2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.5p + 2.5 + p2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.5p + p2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.5p + p2 = 0 + 2.5 -0.5p + p2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.5p + p2 = 2.5 The p term is -0.5p. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5p + 0.0625 + p2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + -0.5p + p2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + -0.5p + p2 = 2.5625 Factor a perfect square on the left side: (p + -0.25)(p + -0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (p + -0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
p + -0.25 = 1.600781059 Simplifying p + -0.25 = 1.600781059 Reorder the terms: -0.25 + p = 1.600781059 Solving -0.25 + p = 1.600781059 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + p = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = 1.600781059 + 0.25 p = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 p = 1.850781059 Simplifying p = 1.850781059Subproblem 2
p + -0.25 = -1.600781059 Simplifying p + -0.25 = -1.600781059 Reorder the terms: -0.25 + p = -1.600781059 Solving -0.25 + p = -1.600781059 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + p = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = -1.600781059 + 0.25 p = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 p = -1.350781059 Simplifying p = -1.350781059Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.850781059, -1.350781059}Solution
p = {1.850781059, -1.350781059}
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