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Simplifying 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 = 8.374281585 X = 8.374281585 Simplifying X = 8.374281585Subproblem 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 = -13.374281585 X = -13.374281585 Simplifying X = -13.374281585Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.374281585, -13.374281585}
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