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Simplifying 2p2 + 18p + -8 = 0 Reorder the terms: -8 + 18p + 2p2 = 0 Solving -8 + 18p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 9p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 9p + p2)' equal to zero and attempt to solve: Simplifying -4 + 9p + p2 = 0 Solving -4 + 9p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 9p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + 9p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 9p + p2 = 0 + 4 9p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 9p + p2 = 4 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 = 4 + 20.25 Reorder the terms: 20.25 + 9p + p2 = 4 + 20.25 Combine like terms: 4 + 20.25 = 24.25 20.25 + 9p + p2 = 24.25 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (p + 4.5) equal to 4.924428901 and -4.924428901.Subproblem 1
p + 4.5 = 4.924428901 Simplifying p + 4.5 = 4.924428901 Reorder the terms: 4.5 + p = 4.924428901 Solving 4.5 + p = 4.924428901 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 = 4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 4.924428901 + -4.5 p = 4.924428901 + -4.5 Combine like terms: 4.924428901 + -4.5 = 0.424428901 p = 0.424428901 Simplifying p = 0.424428901Subproblem 2
p + 4.5 = -4.924428901 Simplifying p + 4.5 = -4.924428901 Reorder the terms: 4.5 + p = -4.924428901 Solving 4.5 + p = -4.924428901 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 = -4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -4.924428901 + -4.5 p = -4.924428901 + -4.5 Combine like terms: -4.924428901 + -4.5 = -9.424428901 p = -9.424428901 Simplifying p = -9.424428901Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.424428901, -9.424428901}Solution
p = {0.424428901, -9.424428901}
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