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Simplifying x * x + -2x + 15 + -1x + 4 = 180 Multiply x * x x2 + -2x + 15 + -1x + 4 = 180 Reorder the terms: 15 + 4 + -2x + -1x + x2 = 180 Combine like terms: 15 + 4 = 19 19 + -2x + -1x + x2 = 180 Combine like terms: -2x + -1x = -3x 19 + -3x + x2 = 180 Solving 19 + -3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 19 + -180 + -3x + x2 = 180 + -180 Combine like terms: 19 + -180 = -161 -161 + -3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -161 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + -3x + 161 + x2 = 0 + 161 Reorder the terms: -161 + 161 + -3x + x2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + -3x + x2 = 0 + 161 -3x + x2 = 0 + 161 Combine like terms: 0 + 161 = 161 -3x + x2 = 161 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 = 161 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 161 + 2.25 Combine like terms: 161 + 2.25 = 163.25 2.25 + -3x + x2 = 163.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 163.25 Calculate the square root of the right side: 12.776932339 Break this problem into two subproblems by setting (x + -1.5) equal to 12.776932339 and -12.776932339.Subproblem 1
x + -1.5 = 12.776932339 Simplifying x + -1.5 = 12.776932339 Reorder the terms: -1.5 + x = 12.776932339 Solving -1.5 + x = 12.776932339 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 = 12.776932339 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.776932339 + 1.5 x = 12.776932339 + 1.5 Combine like terms: 12.776932339 + 1.5 = 14.276932339 x = 14.276932339 Simplifying x = 14.276932339Subproblem 2
x + -1.5 = -12.776932339 Simplifying x + -1.5 = -12.776932339 Reorder the terms: -1.5 + x = -12.776932339 Solving -1.5 + x = -12.776932339 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 = -12.776932339 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.776932339 + 1.5 x = -12.776932339 + 1.5 Combine like terms: -12.776932339 + 1.5 = -11.276932339 x = -11.276932339 Simplifying x = -11.276932339Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.276932339, -11.276932339}
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