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Simplifying 113.097 = x(x + 10) Reorder the terms: 113.097 = x(10 + x) 113.097 = (10 * x + x * x) 113.097 = (10x + x2) Solving 113.097 = 10x + x2 Solving for variable 'x'. Reorder the terms: 113.097 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 113.097 + -10x + -1x2 = 0 + x2 + -1x2 113.097 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 113.097 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -113.097 + 10x + x2 = 0 Move the constant term to the right: Add '113.097' to each side of the equation. -113.097 + 10x + 113.097 + x2 = 0 + 113.097 Reorder the terms: -113.097 + 113.097 + 10x + x2 = 0 + 113.097 Combine like terms: -113.097 + 113.097 = 0.000 0.000 + 10x + x2 = 0 + 113.097 10x + x2 = 0 + 113.097 Combine like terms: 0 + 113.097 = 113.097 10x + x2 = 113.097 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 113.097 + 25 Reorder the terms: 25 + 10x + x2 = 113.097 + 25 Combine like terms: 113.097 + 25 = 138.097 25 + 10x + x2 = 138.097 Factor a perfect square on the left side: (x + 5)(x + 5) = 138.097 Calculate the square root of the right side: 11.751467993 Break this problem into two subproblems by setting (x + 5) equal to 11.751467993 and -11.751467993.Subproblem 1
x + 5 = 11.751467993 Simplifying x + 5 = 11.751467993 Reorder the terms: 5 + x = 11.751467993 Solving 5 + x = 11.751467993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.751467993 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.751467993 + -5 x = 11.751467993 + -5 Combine like terms: 11.751467993 + -5 = 6.751467993 x = 6.751467993 Simplifying x = 6.751467993Subproblem 2
x + 5 = -11.751467993 Simplifying x + 5 = -11.751467993 Reorder the terms: 5 + x = -11.751467993 Solving 5 + x = -11.751467993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.751467993 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.751467993 + -5 x = -11.751467993 + -5 Combine like terms: -11.751467993 + -5 = -16.751467993 x = -16.751467993 Simplifying x = -16.751467993Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.751467993, -16.751467993}
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