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Simplifying (50 + 2x)(30 + 2x) + -150 = 425 Multiply (50 + 2x) * (30 + 2x) (50(30 + 2x) + 2x * (30 + 2x)) + -150 = 425 ((30 * 50 + 2x * 50) + 2x * (30 + 2x)) + -150 = 425 ((1500 + 100x) + 2x * (30 + 2x)) + -150 = 425 (1500 + 100x + (30 * 2x + 2x * 2x)) + -150 = 425 (1500 + 100x + (60x + 4x2)) + -150 = 425 Combine like terms: 100x + 60x = 160x (1500 + 160x + 4x2) + -150 = 425 Reorder the terms: 1500 + -150 + 160x + 4x2 = 425 Combine like terms: 1500 + -150 = 1350 1350 + 160x + 4x2 = 425 Solving 1350 + 160x + 4x2 = 425 Solving for variable 'x'. Reorder the terms: 1350 + -425 + 160x + 4x2 = 425 + -425 Combine like terms: 1350 + -425 = 925 925 + 160x + 4x2 = 425 + -425 Combine like terms: 425 + -425 = 0 925 + 160x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 231.25 + 40x + x2 = 0 Move the constant term to the right: Add '-231.25' to each side of the equation. 231.25 + 40x + -231.25 + x2 = 0 + -231.25 Reorder the terms: 231.25 + -231.25 + 40x + x2 = 0 + -231.25 Combine like terms: 231.25 + -231.25 = 0.00 0.00 + 40x + x2 = 0 + -231.25 40x + x2 = 0 + -231.25 Combine like terms: 0 + -231.25 = -231.25 40x + x2 = -231.25 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -231.25 + 400 Reorder the terms: 400 + 40x + x2 = -231.25 + 400 Combine like terms: -231.25 + 400 = 168.75 400 + 40x + x2 = 168.75 Factor a perfect square on the left side: (x + 20)(x + 20) = 168.75 Calculate the square root of the right side: 12.990381057 Break this problem into two subproblems by setting (x + 20) equal to 12.990381057 and -12.990381057.Subproblem 1
x + 20 = 12.990381057 Simplifying x + 20 = 12.990381057 Reorder the terms: 20 + x = 12.990381057 Solving 20 + x = 12.990381057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 12.990381057 + -20 Combine like terms: 20 + -20 = 0 0 + x = 12.990381057 + -20 x = 12.990381057 + -20 Combine like terms: 12.990381057 + -20 = -7.009618943 x = -7.009618943 Simplifying x = -7.009618943Subproblem 2
x + 20 = -12.990381057 Simplifying x + 20 = -12.990381057 Reorder the terms: 20 + x = -12.990381057 Solving 20 + x = -12.990381057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -12.990381057 + -20 Combine like terms: 20 + -20 = 0 0 + x = -12.990381057 + -20 x = -12.990381057 + -20 Combine like terms: -12.990381057 + -20 = -32.990381057 x = -32.990381057 Simplifying x = -32.990381057Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.009618943, -32.990381057}
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