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Simplifying x2 + -10 + 18 + -3x = 180 Reorder the terms: -10 + 18 + -3x + x2 = 180 Combine like terms: -10 + 18 = 8 8 + -3x + x2 = 180 Solving 8 + -3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 8 + -180 + -3x + x2 = 180 + -180 Combine like terms: 8 + -180 = -172 -172 + -3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -172 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + -3x + 172 + x2 = 0 + 172 Reorder the terms: -172 + 172 + -3x + x2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + -3x + x2 = 0 + 172 -3x + x2 = 0 + 172 Combine like terms: 0 + 172 = 172 -3x + x2 = 172 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 = 172 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 172 + 2.25 Combine like terms: 172 + 2.25 = 174.25 2.25 + -3x + x2 = 174.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -1.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -1.5 = 13.200378782 Simplifying x + -1.5 = 13.200378782 Reorder the terms: -1.5 + x = 13.200378782 Solving -1.5 + x = 13.200378782 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 = 13.200378782 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 13.200378782 + 1.5 x = 13.200378782 + 1.5 Combine like terms: 13.200378782 + 1.5 = 14.700378782 x = 14.700378782 Simplifying x = 14.700378782Subproblem 2
x + -1.5 = -13.200378782 Simplifying x + -1.5 = -13.200378782 Reorder the terms: -1.5 + x = -13.200378782 Solving -1.5 + x = -13.200378782 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 = -13.200378782 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -13.200378782 + 1.5 x = -13.200378782 + 1.5 Combine like terms: -13.200378782 + 1.5 = -11.700378782 x = -11.700378782 Simplifying x = -11.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.700378782, -11.700378782}
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