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Simplifying x2 + 2x + 12 = 180 + -1x Reorder the terms: 12 + 2x + x2 = 180 + -1x Solving 12 + 2x + x2 = 180 + -1x Solving for variable 'x'. Reorder the terms: 12 + -180 + 2x + x + x2 = 180 + -1x + -180 + x Combine like terms: 12 + -180 = -168 -168 + 2x + x + x2 = 180 + -1x + -180 + x Combine like terms: 2x + x = 3x -168 + 3x + x2 = 180 + -1x + -180 + x Reorder the terms: -168 + 3x + x2 = 180 + -180 + -1x + x Combine like terms: 180 + -180 = 0 -168 + 3x + x2 = 0 + -1x + x -168 + 3x + x2 = -1x + x Combine like terms: -1x + x = 0 -168 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 3x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 3x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 3x + x2 = 0 + 168 3x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 3x + x2 = 168 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 = 168 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 168 + 2.25 Combine like terms: 168 + 2.25 = 170.25 2.25 + 3x + x2 = 170.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + 1.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + 1.5 = 13.047988351 Simplifying x + 1.5 = 13.047988351 Reorder the terms: 1.5 + x = 13.047988351 Solving 1.5 + x = 13.047988351 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 = 13.047988351 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.047988351 + -1.5 x = 13.047988351 + -1.5 Combine like terms: 13.047988351 + -1.5 = 11.547988351 x = 11.547988351 Simplifying x = 11.547988351Subproblem 2
x + 1.5 = -13.047988351 Simplifying x + 1.5 = -13.047988351 Reorder the terms: 1.5 + x = -13.047988351 Solving 1.5 + x = -13.047988351 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 = -13.047988351 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.047988351 + -1.5 x = -13.047988351 + -1.5 Combine like terms: -13.047988351 + -1.5 = -14.547988351 x = -14.547988351 Simplifying x = -14.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.547988351, -14.547988351}
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