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Simplifying (50 + x)(30 + x) + -150 = 425 Multiply (50 + x) * (30 + x) (50(30 + x) + x(30 + x)) + -150 = 425 ((30 * 50 + x * 50) + x(30 + x)) + -150 = 425 ((1500 + 50x) + x(30 + x)) + -150 = 425 (1500 + 50x + (30 * x + x * x)) + -150 = 425 (1500 + 50x + (30x + x2)) + -150 = 425 Combine like terms: 50x + 30x = 80x (1500 + 80x + x2) + -150 = 425 Reorder the terms: 1500 + -150 + 80x + x2 = 425 Combine like terms: 1500 + -150 = 1350 1350 + 80x + x2 = 425 Solving 1350 + 80x + x2 = 425 Solving for variable 'x'. Reorder the terms: 1350 + -425 + 80x + x2 = 425 + -425 Combine like terms: 1350 + -425 = 925 925 + 80x + x2 = 425 + -425 Combine like terms: 425 + -425 = 0 925 + 80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-925' to each side of the equation. 925 + 80x + -925 + x2 = 0 + -925 Reorder the terms: 925 + -925 + 80x + x2 = 0 + -925 Combine like terms: 925 + -925 = 0 0 + 80x + x2 = 0 + -925 80x + x2 = 0 + -925 Combine like terms: 0 + -925 = -925 80x + x2 = -925 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -925 + 1600 Reorder the terms: 1600 + 80x + x2 = -925 + 1600 Combine like terms: -925 + 1600 = 675 1600 + 80x + x2 = 675 Factor a perfect square on the left side: (x + 40)(x + 40) = 675 Calculate the square root of the right side: 25.980762114 Break this problem into two subproblems by setting (x + 40) equal to 25.980762114 and -25.980762114.Subproblem 1
x + 40 = 25.980762114 Simplifying x + 40 = 25.980762114 Reorder the terms: 40 + x = 25.980762114 Solving 40 + x = 25.980762114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 25.980762114 + -40 Combine like terms: 40 + -40 = 0 0 + x = 25.980762114 + -40 x = 25.980762114 + -40 Combine like terms: 25.980762114 + -40 = -14.019237886 x = -14.019237886 Simplifying x = -14.019237886Subproblem 2
x + 40 = -25.980762114 Simplifying x + 40 = -25.980762114 Reorder the terms: 40 + x = -25.980762114 Solving 40 + x = -25.980762114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -25.980762114 + -40 Combine like terms: 40 + -40 = 0 0 + x = -25.980762114 + -40 x = -25.980762114 + -40 Combine like terms: -25.980762114 + -40 = -65.980762114 x = -65.980762114 Simplifying x = -65.980762114Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.019237886, -65.980762114}
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