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Simplifying x2 + 3x + -12 = 180 Reorder the terms: -12 + 3x + x2 = 180 Solving -12 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: -12 + -180 + 3x + x2 = 180 + -180 Combine like terms: -12 + -180 = -192 -192 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -192 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 3x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 3x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 3x + x2 = 0 + 192 3x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 3x + x2 = 192 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 = 192 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 192 + 2.25 Combine like terms: 192 + 2.25 = 194.25 2.25 + 3x + x2 = 194.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 194.25 Calculate the square root of the right side: 13.937359865 Break this problem into two subproblems by setting (x + 1.5) equal to 13.937359865 and -13.937359865.Subproblem 1
x + 1.5 = 13.937359865 Simplifying x + 1.5 = 13.937359865 Reorder the terms: 1.5 + x = 13.937359865 Solving 1.5 + x = 13.937359865 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 = 13.937359865 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.937359865 + -1.5 x = 13.937359865 + -1.5 Combine like terms: 13.937359865 + -1.5 = 12.437359865 x = 12.437359865 Simplifying x = 12.437359865Subproblem 2
x + 1.5 = -13.937359865 Simplifying x + 1.5 = -13.937359865 Reorder the terms: 1.5 + x = -13.937359865 Solving 1.5 + x = -13.937359865 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 = -13.937359865 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.937359865 + -1.5 x = -13.937359865 + -1.5 Combine like terms: -13.937359865 + -1.5 = -15.437359865 x = -15.437359865 Simplifying x = -15.437359865Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.437359865, -15.437359865}
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