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Simplifying p2 + 7p + -12 = 0 Reorder the terms: -12 + 7p + p2 = 0 Solving -12 + 7p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 7p + 12 + p2 = 0 + 12 Reorder the terms: -12 + 12 + 7p + p2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7p + p2 = 0 + 12 7p + p2 = 0 + 12 Combine like terms: 0 + 12 = 12 7p + p2 = 12 The p term is 7p. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7p + 12.25 + p2 = 12 + 12.25 Reorder the terms: 12.25 + 7p + p2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + 7p + p2 = 24.25 Factor a perfect square on the left side: (p + 3.5)(p + 3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (p + 3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
p + 3.5 = 4.924428901 Simplifying p + 3.5 = 4.924428901 Reorder the terms: 3.5 + p = 4.924428901 Solving 3.5 + p = 4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = 4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = 4.924428901 + -3.5 p = 4.924428901 + -3.5 Combine like terms: 4.924428901 + -3.5 = 1.424428901 p = 1.424428901 Simplifying p = 1.424428901Subproblem 2
p + 3.5 = -4.924428901 Simplifying p + 3.5 = -4.924428901 Reorder the terms: 3.5 + p = -4.924428901 Solving 3.5 + p = -4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = -4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = -4.924428901 + -3.5 p = -4.924428901 + -3.5 Combine like terms: -4.924428901 + -3.5 = -8.424428901 p = -8.424428901 Simplifying p = -8.424428901Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.424428901, -8.424428901}
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