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Simplifying 2p2 + -18p + 2 = 0 Reorder the terms: 2 + -18p + 2p2 = 0 Solving 2 + -18p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -9p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -9p + p2)' equal to zero and attempt to solve: Simplifying 1 + -9p + p2 = 0 Solving 1 + -9p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -9p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -9p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9p + p2 = 0 + -1 -9p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9p + p2 = -1 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = -1 + 20.25 Reorder the terms: 20.25 + -9p + p2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + -9p + p2 = 19.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (p + -4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
p + -4.5 = 4.387482194 Simplifying p + -4.5 = 4.387482194 Reorder the terms: -4.5 + p = 4.387482194 Solving -4.5 + p = 4.387482194 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 4.387482194 + 4.5 p = 4.387482194 + 4.5 Combine like terms: 4.387482194 + 4.5 = 8.887482194 p = 8.887482194 Simplifying p = 8.887482194Subproblem 2
p + -4.5 = -4.387482194 Simplifying p + -4.5 = -4.387482194 Reorder the terms: -4.5 + p = -4.387482194 Solving -4.5 + p = -4.387482194 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -4.387482194 + 4.5 p = -4.387482194 + 4.5 Combine like terms: -4.387482194 + 4.5 = 0.112517806 p = 0.112517806 Simplifying p = 0.112517806Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.887482194, 0.112517806}Solution
p = {8.887482194, 0.112517806}
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