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Simplifying (x2) + 3x + 13 = 182 x2 + 3x + 13 = 182 Reorder the terms: 13 + 3x + x2 = 182 Solving 13 + 3x + x2 = 182 Solving for variable 'x'. Reorder the terms: 13 + -182 + 3x + x2 = 182 + -182 Combine like terms: 13 + -182 = -169 -169 + 3x + x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -169 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + 3x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 3x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 3x + x2 = 0 + 169 3x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 3x + x2 = 169 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 169 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 169 + 2.25 Combine like terms: 169 + 2.25 = 171.25 2.25 + 3x + x2 = 171.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 171.25 Calculate the square root of the right side: 13.086252328 Break this problem into two subproblems by setting (x + 1.5) equal to 13.086252328 and -13.086252328.Subproblem 1
x + 1.5 = 13.086252328 Simplifying x + 1.5 = 13.086252328 Reorder the terms: 1.5 + x = 13.086252328 Solving 1.5 + x = 13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 13.086252328 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.086252328 + -1.5 x = 13.086252328 + -1.5 Combine like terms: 13.086252328 + -1.5 = 11.586252328 x = 11.586252328 Simplifying x = 11.586252328Subproblem 2
x + 1.5 = -13.086252328 Simplifying x + 1.5 = -13.086252328 Reorder the terms: 1.5 + x = -13.086252328 Solving 1.5 + x = -13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -13.086252328 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.086252328 + -1.5 x = -13.086252328 + -1.5 Combine like terms: -13.086252328 + -1.5 = -14.586252328 x = -14.586252328 Simplifying x = -14.586252328Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.586252328, -14.586252328}
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