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Simplifying (x) = x2 + 26x + -56 x = x2 + 26x + -56 Reorder the terms: x = -56 + 26x + x2 Solving x = -56 + 26x + x2 Solving for variable 'x'. Reorder the terms: 56 + x + -26x + -1x2 = -56 + 26x + x2 + 56 + -26x + -1x2 Combine like terms: x + -26x = -25x 56 + -25x + -1x2 = -56 + 26x + x2 + 56 + -26x + -1x2 Reorder the terms: 56 + -25x + -1x2 = -56 + 56 + 26x + -26x + x2 + -1x2 Combine like terms: -56 + 56 = 0 56 + -25x + -1x2 = 0 + 26x + -26x + x2 + -1x2 56 + -25x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 56 + -25x + -1x2 = 0 + x2 + -1x2 56 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 56 + -25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -56 + 25x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 25x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 25x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 25x + x2 = 0 + 56 25x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 25x + x2 = 56 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 56 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 56 + 156.25 Combine like terms: 56 + 156.25 = 212.25 156.25 + 25x + x2 = 212.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 212.25 Calculate the square root of the right side: 14.568802284 Break this problem into two subproblems by setting (x + 12.5) equal to 14.568802284 and -14.568802284.Subproblem 1
x + 12.5 = 14.568802284 Simplifying x + 12.5 = 14.568802284 Reorder the terms: 12.5 + x = 14.568802284 Solving 12.5 + x = 14.568802284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 14.568802284 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 14.568802284 + -12.5 x = 14.568802284 + -12.5 Combine like terms: 14.568802284 + -12.5 = 2.068802284 x = 2.068802284 Simplifying x = 2.068802284Subproblem 2
x + 12.5 = -14.568802284 Simplifying x + 12.5 = -14.568802284 Reorder the terms: 12.5 + x = -14.568802284 Solving 12.5 + x = -14.568802284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -14.568802284 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -14.568802284 + -12.5 x = -14.568802284 + -12.5 Combine like terms: -14.568802284 + -12.5 = -27.068802284 x = -27.068802284 Simplifying x = -27.068802284Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.068802284, -27.068802284}
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