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Simplifying 5x + -1x2 = -168 Solving 5x + -1x2 = -168 Solving for variable 'x'. Reorder the terms: 168 + 5x + -1x2 = -168 + 168 Combine like terms: -168 + 168 = 0 168 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -168 + -5x + x2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -5x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -5x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -5x + x2 = 0 + 168 -5x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -5x + x2 = 168 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 168 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 168 + 6.25 Combine like terms: 168 + 6.25 = 174.25 6.25 + -5x + x2 = 174.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -2.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -2.5 = 13.200378782 Simplifying x + -2.5 = 13.200378782 Reorder the terms: -2.5 + x = 13.200378782 Solving -2.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 13.200378782 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 13.200378782 + 2.5 x = 13.200378782 + 2.5 Combine like terms: 13.200378782 + 2.5 = 15.700378782 x = 15.700378782 Simplifying x = 15.700378782Subproblem 2
x + -2.5 = -13.200378782 Simplifying x + -2.5 = -13.200378782 Reorder the terms: -2.5 + x = -13.200378782 Solving -2.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -13.200378782 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -13.200378782 + 2.5 x = -13.200378782 + 2.5 Combine like terms: -13.200378782 + 2.5 = -10.700378782 x = -10.700378782 Simplifying x = -10.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.700378782, -10.700378782}
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