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Simplifying x2 + 17x + -12 = 0 Reorder the terms: -12 + 17x + x2 = 0 Solving -12 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 17x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 17x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 17x + x2 = 0 + 12 17x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 17x + x2 = 12 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 12 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 12 + 72.25 Combine like terms: 12 + 72.25 = 84.25 72.25 + 17x + x2 = 84.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 8.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 8.5 = 9.178779875 Simplifying x + 8.5 = 9.178779875 Reorder the terms: 8.5 + x = 9.178779875 Solving 8.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 9.178779875 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.178779875 + -8.5 x = 9.178779875 + -8.5 Combine like terms: 9.178779875 + -8.5 = 0.678779875 x = 0.678779875 Simplifying x = 0.678779875Subproblem 2
x + 8.5 = -9.178779875 Simplifying x + 8.5 = -9.178779875 Reorder the terms: 8.5 + x = -9.178779875 Solving 8.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -9.178779875 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.178779875 + -8.5 x = -9.178779875 + -8.5 Combine like terms: -9.178779875 + -8.5 = -17.678779875 x = -17.678779875 Simplifying x = -17.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.678779875, -17.678779875}
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