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Simplifying x2 + -2x + 9x + 131 = 180 Reorder the terms: 131 + -2x + 9x + x2 = 180 Combine like terms: -2x + 9x = 7x 131 + 7x + x2 = 180 Solving 131 + 7x + x2 = 180 Solving for variable 'x'. Reorder the terms: 131 + -180 + 7x + x2 = 180 + -180 Combine like terms: 131 + -180 = -49 -49 + 7x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -49 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 7x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 7x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 7x + x2 = 0 + 49 7x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 7x + x2 = 49 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 49 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 49 + 12.25 Combine like terms: 49 + 12.25 = 61.25 12.25 + 7x + x2 = 61.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 3.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 3.5 = 7.826237921 Simplifying x + 3.5 = 7.826237921 Reorder the terms: 3.5 + x = 7.826237921 Solving 3.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.826237921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.826237921 + -3.5 x = 7.826237921 + -3.5 Combine like terms: 7.826237921 + -3.5 = 4.326237921 x = 4.326237921 Simplifying x = 4.326237921Subproblem 2
x + 3.5 = -7.826237921 Simplifying x + 3.5 = -7.826237921 Reorder the terms: 3.5 + x = -7.826237921 Solving 3.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.826237921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.826237921 + -3.5 x = -7.826237921 + -3.5 Combine like terms: -7.826237921 + -3.5 = -11.326237921 x = -11.326237921 Simplifying x = -11.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.326237921, -11.326237921}
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