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Simplifying (10 + x)(50 + x)(2) = 150 Reorder the terms for easier multiplication: 2(10 + x)(50 + x) = 150 Multiply (10 + x) * (50 + x) 2(10(50 + x) + x(50 + x)) = 150 2((50 * 10 + x * 10) + x(50 + x)) = 150 2((500 + 10x) + x(50 + x)) = 150 2(500 + 10x + (50 * x + x * x)) = 150 2(500 + 10x + (50x + x2)) = 150 Combine like terms: 10x + 50x = 60x 2(500 + 60x + x2) = 150 (500 * 2 + 60x * 2 + x2 * 2) = 150 (1000 + 120x + 2x2) = 150 Solving 1000 + 120x + 2x2 = 150 Solving for variable 'x'. Reorder the terms: 1000 + -150 + 120x + 2x2 = 150 + -150 Combine like terms: 1000 + -150 = 850 850 + 120x + 2x2 = 150 + -150 Combine like terms: 150 + -150 = 0 850 + 120x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(425 + 60x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(425 + 60x + x2)' equal to zero and attempt to solve: Simplifying 425 + 60x + x2 = 0 Solving 425 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-425' to each side of the equation. 425 + 60x + -425 + x2 = 0 + -425 Reorder the terms: 425 + -425 + 60x + x2 = 0 + -425 Combine like terms: 425 + -425 = 0 0 + 60x + x2 = 0 + -425 60x + x2 = 0 + -425 Combine like terms: 0 + -425 = -425 60x + x2 = -425 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -425 + 900 Reorder the terms: 900 + 60x + x2 = -425 + 900 Combine like terms: -425 + 900 = 475 900 + 60x + x2 = 475 Factor a perfect square on the left side: (x + 30)(x + 30) = 475 Calculate the square root of the right side: 21.794494718 Break this problem into two subproblems by setting (x + 30) equal to 21.794494718 and -21.794494718.Subproblem 1
x + 30 = 21.794494718 Simplifying x + 30 = 21.794494718 Reorder the terms: 30 + x = 21.794494718 Solving 30 + x = 21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 21.794494718 + -30 Combine like terms: 30 + -30 = 0 0 + x = 21.794494718 + -30 x = 21.794494718 + -30 Combine like terms: 21.794494718 + -30 = -8.205505282 x = -8.205505282 Simplifying x = -8.205505282Subproblem 2
x + 30 = -21.794494718 Simplifying x + 30 = -21.794494718 Reorder the terms: 30 + x = -21.794494718 Solving 30 + x = -21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -21.794494718 + -30 Combine like terms: 30 + -30 = 0 0 + x = -21.794494718 + -30 x = -21.794494718 + -30 Combine like terms: -21.794494718 + -30 = -51.794494718 x = -51.794494718 Simplifying x = -51.794494718Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.205505282, -51.794494718}Solution
x = {-8.205505282, -51.794494718}
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