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Simplifying 112 = x(x + -5) Reorder the terms: 112 = x(-5 + x) 112 = (-5 * x + x * x) 112 = (-5x + x2) Solving 112 = -5x + x2 Solving for variable 'x'. Reorder the terms: 112 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 112 + 5x + -1x2 = 0 + x2 + -1x2 112 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 112 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -112 + -5x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + -5x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -5x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -5x + x2 = 0 + 112 -5x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -5x + x2 = 112 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 = 112 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 112 + 6.25 Combine like terms: 112 + 6.25 = 118.25 6.25 + -5x + x2 = 118.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + -2.5) equal to 10.874281585 and -10.874281585.Subproblem 1
x + -2.5 = 10.874281585 Simplifying x + -2.5 = 10.874281585 Reorder the terms: -2.5 + x = 10.874281585 Solving -2.5 + x = 10.874281585 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 = 10.874281585 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.874281585 + 2.5 x = 10.874281585 + 2.5 Combine like terms: 10.874281585 + 2.5 = 13.374281585 x = 13.374281585 Simplifying x = 13.374281585Subproblem 2
x + -2.5 = -10.874281585 Simplifying x + -2.5 = -10.874281585 Reorder the terms: -2.5 + x = -10.874281585 Solving -2.5 + x = -10.874281585 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 = -10.874281585 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.874281585 + 2.5 x = -10.874281585 + 2.5 Combine like terms: -10.874281585 + 2.5 = -8.374281585 x = -8.374281585 Simplifying x = -8.374281585Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.374281585, -8.374281585}
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