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Simplifying 120x = (x + 2)(120 + -1x) Reorder the terms: 120x = (2 + x)(120 + -1x) Multiply (2 + x) * (120 + -1x) 120x = (2(120 + -1x) + x(120 + -1x)) 120x = ((120 * 2 + -1x * 2) + x(120 + -1x)) 120x = ((240 + -2x) + x(120 + -1x)) 120x = (240 + -2x + (120 * x + -1x * x)) 120x = (240 + -2x + (120x + -1x2)) Combine like terms: -2x + 120x = 118x 120x = (240 + 118x + -1x2) Solving 120x = 240 + 118x + -1x2 Solving for variable 'x'. Reorder the terms: -240 + 120x + -118x + x2 = 240 + 118x + -1x2 + -240 + -118x + x2 Combine like terms: 120x + -118x = 2x -240 + 2x + x2 = 240 + 118x + -1x2 + -240 + -118x + x2 Reorder the terms: -240 + 2x + x2 = 240 + -240 + 118x + -118x + -1x2 + x2 Combine like terms: 240 + -240 = 0 -240 + 2x + x2 = 0 + 118x + -118x + -1x2 + x2 -240 + 2x + x2 = 118x + -118x + -1x2 + x2 Combine like terms: 118x + -118x = 0 -240 + 2x + x2 = 0 + -1x2 + x2 -240 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -240 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 2x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 2x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 2x + x2 = 0 + 240 2x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 2x + x2 = 240 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 240 + 1 Reorder the terms: 1 + 2x + x2 = 240 + 1 Combine like terms: 240 + 1 = 241 1 + 2x + x2 = 241 Factor a perfect square on the left side: (x + 1)(x + 1) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 1) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 1 = 15.524174696 Simplifying x + 1 = 15.524174696 Reorder the terms: 1 + x = 15.524174696 Solving 1 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.524174696 + -1 x = 15.524174696 + -1 Combine like terms: 15.524174696 + -1 = 14.524174696 x = 14.524174696 Simplifying x = 14.524174696Subproblem 2
x + 1 = -15.524174696 Simplifying x + 1 = -15.524174696 Reorder the terms: 1 + x = -15.524174696 Solving 1 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.524174696 + -1 x = -15.524174696 + -1 Combine like terms: -15.524174696 + -1 = -16.524174696 x = -16.524174696 Simplifying x = -16.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.524174696, -16.524174696}
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