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Simplifying (x + 7)(x + -2) = 118 Reorder the terms: (7 + x)(x + -2) = 118 Reorder the terms: (7 + x)(-2 + x) = 118 Multiply (7 + x) * (-2 + x) (7(-2 + x) + x(-2 + x)) = 118 ((-2 * 7 + x * 7) + x(-2 + x)) = 118 ((-14 + 7x) + x(-2 + x)) = 118 (-14 + 7x + (-2 * x + x * x)) = 118 (-14 + 7x + (-2x + x2)) = 118 Combine like terms: 7x + -2x = 5x (-14 + 5x + x2) = 118 Solving -14 + 5x + x2 = 118 Solving for variable 'x'. Reorder the terms: -14 + -118 + 5x + x2 = 118 + -118 Combine like terms: -14 + -118 = -132 -132 + 5x + x2 = 118 + -118 Combine like terms: 118 + -118 = 0 -132 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + 5x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + 5x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 5x + x2 = 0 + 132 5x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 5x + x2 = 132 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 = 132 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 132 + 6.25 Combine like terms: 132 + 6.25 = 138.25 6.25 + 5x + x2 = 138.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + 2.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + 2.5 = 11.757976016 Simplifying x + 2.5 = 11.757976016 Reorder the terms: 2.5 + x = 11.757976016 Solving 2.5 + x = 11.757976016 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 = 11.757976016 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.757976016 + -2.5 x = 11.757976016 + -2.5 Combine like terms: 11.757976016 + -2.5 = 9.257976016 x = 9.257976016 Simplifying x = 9.257976016Subproblem 2
x + 2.5 = -11.757976016 Simplifying x + 2.5 = -11.757976016 Reorder the terms: 2.5 + x = -11.757976016 Solving 2.5 + x = -11.757976016 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 = -11.757976016 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.757976016 + -2.5 x = -11.757976016 + -2.5 Combine like terms: -11.757976016 + -2.5 = -14.257976016 x = -14.257976016 Simplifying x = -14.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.257976016, -14.257976016}
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