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Simplifying x2 + -1x + 11 = 180 Reorder the terms: 11 + -1x + x2 = 180 Solving 11 + -1x + x2 = 180 Solving for variable 'x'. Reorder the terms: 11 + -180 + -1x + x2 = 180 + -180 Combine like terms: 11 + -180 = -169 -169 + -1x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -169 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + -1x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + -1x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + -1x + x2 = 0 + 169 -1x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 -1x + x2 = 169 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 169 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 169 + 0.25 Combine like terms: 169 + 0.25 = 169.25 0.25 + -1x + x2 = 169.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 169.25 Calculate the square root of the right side: 13.009611831 Break this problem into two subproblems by setting (x + -0.5) equal to 13.009611831 and -13.009611831.Subproblem 1
x + -0.5 = 13.009611831 Simplifying x + -0.5 = 13.009611831 Reorder the terms: -0.5 + x = 13.009611831 Solving -0.5 + x = 13.009611831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 13.009611831 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 13.009611831 + 0.5 x = 13.009611831 + 0.5 Combine like terms: 13.009611831 + 0.5 = 13.509611831 x = 13.509611831 Simplifying x = 13.509611831Subproblem 2
x + -0.5 = -13.009611831 Simplifying x + -0.5 = -13.009611831 Reorder the terms: -0.5 + x = -13.009611831 Solving -0.5 + x = -13.009611831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -13.009611831 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -13.009611831 + 0.5 x = -13.009611831 + 0.5 Combine like terms: -13.009611831 + 0.5 = -12.509611831 x = -12.509611831 Simplifying x = -12.509611831Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.509611831, -12.509611831}
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