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Simplifying x2 + 9x + -2 = 180 Reorder the terms: -2 + 9x + x2 = 180 Solving -2 + 9x + x2 = 180 Solving for variable 'x'. Reorder the terms: -2 + -180 + 9x + x2 = 180 + -180 Combine like terms: -2 + -180 = -182 -182 + 9x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -182 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '182' to each side of the equation. -182 + 9x + 182 + x2 = 0 + 182 Reorder the terms: -182 + 182 + 9x + x2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 9x + x2 = 0 + 182 9x + x2 = 0 + 182 Combine like terms: 0 + 182 = 182 9x + x2 = 182 The x term is 9x. 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. 9x + 20.25 + x2 = 182 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 182 + 20.25 Combine like terms: 182 + 20.25 = 202.25 20.25 + 9x + x2 = 202.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + 4.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + 4.5 = 14.221462653 Simplifying x + 4.5 = 14.221462653 Reorder the terms: 4.5 + x = 14.221462653 Solving 4.5 + x = 14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 14.221462653 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 14.221462653 + -4.5 x = 14.221462653 + -4.5 Combine like terms: 14.221462653 + -4.5 = 9.721462653 x = 9.721462653 Simplifying x = 9.721462653Subproblem 2
x + 4.5 = -14.221462653 Simplifying x + 4.5 = -14.221462653 Reorder the terms: 4.5 + x = -14.221462653 Solving 4.5 + x = -14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -14.221462653 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -14.221462653 + -4.5 x = -14.221462653 + -4.5 Combine like terms: -14.221462653 + -4.5 = -18.721462653 x = -18.721462653 Simplifying x = -18.721462653Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.721462653, -18.721462653}
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