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Simplifying 8p2 + -4p + -20 = -6 Reorder the terms: -20 + -4p + 8p2 = -6 Solving -20 + -4p + 8p2 = -6 Solving for variable 'p'. Reorder the terms: -20 + 6 + -4p + 8p2 = -6 + 6 Combine like terms: -20 + 6 = -14 -14 + -4p + 8p2 = -6 + 6 Combine like terms: -6 + 6 = 0 -14 + -4p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -2p + 4p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -2p + 4p2)' equal to zero and attempt to solve: Simplifying -7 + -2p + 4p2 = 0 Solving -7 + -2p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -0.5p + p2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.5p + 1.75 + p2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.5p + p2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.5p + p2 = 0 + 1.75 -0.5p + p2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.5p + p2 = 1.75 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 = 1.75 + 0.0625 Reorder the terms: 0.0625 + -0.5p + p2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + -0.5p + p2 = 1.8125 Factor a perfect square on the left side: (p + -0.25)(p + -0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (p + -0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
p + -0.25 = 1.346291202 Simplifying p + -0.25 = 1.346291202 Reorder the terms: -0.25 + p = 1.346291202 Solving -0.25 + p = 1.346291202 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 = 1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = 1.346291202 + 0.25 p = 1.346291202 + 0.25 Combine like terms: 1.346291202 + 0.25 = 1.596291202 p = 1.596291202 Simplifying p = 1.596291202Subproblem 2
p + -0.25 = -1.346291202 Simplifying p + -0.25 = -1.346291202 Reorder the terms: -0.25 + p = -1.346291202 Solving -0.25 + p = -1.346291202 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 = -1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = -1.346291202 + 0.25 p = -1.346291202 + 0.25 Combine like terms: -1.346291202 + 0.25 = -1.096291202 p = -1.096291202 Simplifying p = -1.096291202Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.596291202, -1.096291202}Solution
p = {1.596291202, -1.096291202}
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