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Simplifying 0 = x2 + -1x + -174 Reorder the terms: 0 = -174 + -1x + x2 Solving 0 = -174 + -1x + x2 Solving for variable 'x'. Combine like terms: 0 + 174 = 174 174 + x + -1x2 = -174 + -1x + x2 + 174 + x + -1x2 Reorder the terms: 174 + x + -1x2 = -174 + 174 + -1x + x + x2 + -1x2 Combine like terms: -174 + 174 = 0 174 + x + -1x2 = 0 + -1x + x + x2 + -1x2 174 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 174 + x + -1x2 = 0 + x2 + -1x2 174 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 174 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -174 + -1x + x2 = 0 Move the constant term to the right: Add '174' to each side of the equation. -174 + -1x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + -1x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + -1x + x2 = 0 + 174 -1x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 -1x + x2 = 174 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 = 174 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 174 + 0.25 Combine like terms: 174 + 0.25 = 174.25 0.25 + -1x + x2 = 174.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + 0.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + 0.5 = 13.200378782 Simplifying x + 0.5 = 13.200378782 Reorder the terms: 0.5 + x = 13.200378782 Solving 0.5 + x = 13.200378782 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 = 13.200378782 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.200378782 + -0.5 x = 13.200378782 + -0.5 Combine like terms: 13.200378782 + -0.5 = 12.700378782 x = 12.700378782 Simplifying x = 12.700378782Subproblem 2
x + 0.5 = -13.200378782 Simplifying x + 0.5 = -13.200378782 Reorder the terms: 0.5 + x = -13.200378782 Solving 0.5 + x = -13.200378782 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 = -13.200378782 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.200378782 + -0.5 x = -13.200378782 + -0.5 Combine like terms: -13.200378782 + -0.5 = -13.700378782 x = -13.700378782 Simplifying x = -13.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.700378782, -13.700378782}
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