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Simplifying x2 + -2 + 3x + 8 = 180 Reorder the terms: -2 + 8 + 3x + x2 = 180 Combine like terms: -2 + 8 = 6 6 + 3x + x2 = 180 Solving 6 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + 3x + x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '174' to each side of the equation. -174 + 3x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 3x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 3x + x2 = 0 + 174 3x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 3x + x2 = 174 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 = 174 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 174 + 2.25 Combine like terms: 174 + 2.25 = 176.25 2.25 + 3x + x2 = 176.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (x + 1.5) equal to 13.275918047 and -13.275918047.Subproblem 1
x + 1.5 = 13.275918047 Simplifying x + 1.5 = 13.275918047 Reorder the terms: 1.5 + x = 13.275918047 Solving 1.5 + x = 13.275918047 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 = 13.275918047 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.275918047 + -1.5 x = 13.275918047 + -1.5 Combine like terms: 13.275918047 + -1.5 = 11.775918047 x = 11.775918047 Simplifying x = 11.775918047Subproblem 2
x + 1.5 = -13.275918047 Simplifying x + 1.5 = -13.275918047 Reorder the terms: 1.5 + x = -13.275918047 Solving 1.5 + x = -13.275918047 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 = -13.275918047 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.275918047 + -1.5 x = -13.275918047 + -1.5 Combine like terms: -13.275918047 + -1.5 = -14.775918047 x = -14.775918047 Simplifying x = -14.775918047Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.775918047, -14.775918047}
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