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Simplifying x = x2 + 7 + -143 Reorder the terms: x = 7 + -143 + x2 Combine like terms: 7 + -143 = -136 x = -136 + x2 Solving x = -136 + x2 Solving for variable 'x'. Reorder the terms: 136 + x + -1x2 = -136 + x2 + 136 + -1x2 Reorder the terms: 136 + x + -1x2 = -136 + 136 + x2 + -1x2 Combine like terms: -136 + 136 = 0 136 + x + -1x2 = 0 + x2 + -1x2 136 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 136 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -136 + -1x + x2 = 0 Move the constant term to the right: Add '136' to each side of the equation. -136 + -1x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + -1x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -1x + x2 = 0 + 136 -1x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 -1x + x2 = 136 The x term is x. 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 = 136 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 136 + 0.25 Combine like terms: 136 + 0.25 = 136.25 0.25 + -1x + x2 = 136.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + 0.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + 0.5 = 11.67261753 Simplifying x + 0.5 = 11.67261753 Reorder the terms: 0.5 + x = 11.67261753 Solving 0.5 + x = 11.67261753 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 = 11.67261753 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.67261753 + -0.5 x = 11.67261753 + -0.5 Combine like terms: 11.67261753 + -0.5 = 11.17261753 x = 11.17261753 Simplifying x = 11.17261753Subproblem 2
x + 0.5 = -11.67261753 Simplifying x + 0.5 = -11.67261753 Reorder the terms: 0.5 + x = -11.67261753 Solving 0.5 + x = -11.67261753 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 = -11.67261753 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.67261753 + -0.5 x = -11.67261753 + -0.5 Combine like terms: -11.67261753 + -0.5 = -12.17261753 x = -12.17261753 Simplifying x = -12.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.17261753, -12.17261753}
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