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Simplifying x = (200 + -10x)(10 + x) Multiply (200 + -10x) * (10 + x) x = (200(10 + x) + -10x * (10 + x)) x = ((10 * 200 + x * 200) + -10x * (10 + x)) x = ((2000 + 200x) + -10x * (10 + x)) x = (2000 + 200x + (10 * -10x + x * -10x)) x = (2000 + 200x + (-100x + -10x2)) Combine like terms: 200x + -100x = 100x x = (2000 + 100x + -10x2) Solving x = 2000 + 100x + -10x2 Solving for variable 'x'. Reorder the terms: -2000 + x + -100x + 10x2 = 2000 + 100x + -10x2 + -2000 + -100x + 10x2 Combine like terms: x + -100x = -99x -2000 + -99x + 10x2 = 2000 + 100x + -10x2 + -2000 + -100x + 10x2 Reorder the terms: -2000 + -99x + 10x2 = 2000 + -2000 + 100x + -100x + -10x2 + 10x2 Combine like terms: 2000 + -2000 = 0 -2000 + -99x + 10x2 = 0 + 100x + -100x + -10x2 + 10x2 -2000 + -99x + 10x2 = 100x + -100x + -10x2 + 10x2 Combine like terms: 100x + -100x = 0 -2000 + -99x + 10x2 = 0 + -10x2 + 10x2 -2000 + -99x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -2000 + -99x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -200 + -9.9x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -9.9x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -9.9x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -9.9x + x2 = 0 + 200 -9.9x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -9.9x + x2 = 200 The x term is -9.9x. Take half its coefficient (-4.95). Square it (24.5025) and add it to both sides. Add '24.5025' to each side of the equation. -9.9x + 24.5025 + x2 = 200 + 24.5025 Reorder the terms: 24.5025 + -9.9x + x2 = 200 + 24.5025 Combine like terms: 200 + 24.5025 = 224.5025 24.5025 + -9.9x + x2 = 224.5025 Factor a perfect square on the left side: (x + -4.95)(x + -4.95) = 224.5025 Calculate the square root of the right side: 14.98340749 Break this problem into two subproblems by setting (x + -4.95) equal to 14.98340749 and -14.98340749.Subproblem 1
x + -4.95 = 14.98340749 Simplifying x + -4.95 = 14.98340749 Reorder the terms: -4.95 + x = 14.98340749 Solving -4.95 + x = 14.98340749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.95' to each side of the equation. -4.95 + 4.95 + x = 14.98340749 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + x = 14.98340749 + 4.95 x = 14.98340749 + 4.95 Combine like terms: 14.98340749 + 4.95 = 19.93340749 x = 19.93340749 Simplifying x = 19.93340749Subproblem 2
x + -4.95 = -14.98340749 Simplifying x + -4.95 = -14.98340749 Reorder the terms: -4.95 + x = -14.98340749 Solving -4.95 + x = -14.98340749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.95' to each side of the equation. -4.95 + 4.95 + x = -14.98340749 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + x = -14.98340749 + 4.95 x = -14.98340749 + 4.95 Combine like terms: -14.98340749 + 4.95 = -10.03340749 x = -10.03340749 Simplifying x = -10.03340749Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.93340749, -10.03340749}
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