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Simplifying (16 + -1x)(10 + -1x) = 120 Multiply (16 + -1x) * (10 + -1x) (16(10 + -1x) + -1x * (10 + -1x)) = 120 ((10 * 16 + -1x * 16) + -1x * (10 + -1x)) = 120 ((160 + -16x) + -1x * (10 + -1x)) = 120 (160 + -16x + (10 * -1x + -1x * -1x)) = 120 (160 + -16x + (-10x + 1x2)) = 120 Combine like terms: -16x + -10x = -26x (160 + -26x + 1x2) = 120 Solving 160 + -26x + 1x2 = 120 Solving for variable 'x'. Reorder the terms: 160 + -120 + -26x + 1x2 = 120 + -120 Combine like terms: 160 + -120 = 40 40 + -26x + 1x2 = 120 + -120 Combine like terms: 120 + -120 = 0 40 + -26x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -26x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -26x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -26x + x2 = 0 + -40 -26x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -26x + x2 = -40 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -40 + 169 Reorder the terms: 169 + -26x + x2 = -40 + 169 Combine like terms: -40 + 169 = 129 169 + -26x + x2 = 129 Factor a perfect square on the left side: (x + -13)(x + -13) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -13) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -13 = 11.357816692 Simplifying x + -13 = 11.357816692 Reorder the terms: -13 + x = 11.357816692 Solving -13 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 11.357816692 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.357816692 + 13 x = 11.357816692 + 13 Combine like terms: 11.357816692 + 13 = 24.357816692 x = 24.357816692 Simplifying x = 24.357816692Subproblem 2
x + -13 = -11.357816692 Simplifying x + -13 = -11.357816692 Reorder the terms: -13 + x = -11.357816692 Solving -13 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -11.357816692 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.357816692 + 13 x = -11.357816692 + 13 Combine like terms: -11.357816692 + 13 = 1.642183308 x = 1.642183308 Simplifying x = 1.642183308Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.357816692, 1.642183308}
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