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Simplifying 16p2 + -16p + -20 = 0 Reorder the terms: -20 + -16p + 16p2 = 0 Solving -20 + -16p + 16p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -4p + 4p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -4p + 4p2)' equal to zero and attempt to solve: Simplifying -5 + -4p + 4p2 = 0 Solving -5 + -4p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1p + p2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1p + 1.25 + p2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1p + p2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1p + p2 = 0 + 1.25 -1p + p2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1p + p2 = 1.25 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 1.25 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 0.25 + -1p + p2 = 1.5 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (p + -0.5) equal to 1.224744871 and -1.224744871.Subproblem 1
p + -0.5 = 1.224744871 Simplifying p + -0.5 = 1.224744871 Reorder the terms: -0.5 + p = 1.224744871 Solving -0.5 + p = 1.224744871 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.224744871 + 0.5 p = 1.224744871 + 0.5 Combine like terms: 1.224744871 + 0.5 = 1.724744871 p = 1.724744871 Simplifying p = 1.724744871Subproblem 2
p + -0.5 = -1.224744871 Simplifying p + -0.5 = -1.224744871 Reorder the terms: -0.5 + p = -1.224744871 Solving -0.5 + p = -1.224744871 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.224744871 + 0.5 p = -1.224744871 + 0.5 Combine like terms: -1.224744871 + 0.5 = -0.724744871 p = -0.724744871 Simplifying p = -0.724744871Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.724744871, -0.724744871}Solution
p = {1.724744871, -0.724744871}
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