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Simplifying (140 + x)(90 + x) = 3654 Multiply (140 + x) * (90 + x) (140(90 + x) + x(90 + x)) = 3654 ((90 * 140 + x * 140) + x(90 + x)) = 3654 ((12600 + 140x) + x(90 + x)) = 3654 (12600 + 140x + (90 * x + x * x)) = 3654 (12600 + 140x + (90x + x2)) = 3654 Combine like terms: 140x + 90x = 230x (12600 + 230x + x2) = 3654 Solving 12600 + 230x + x2 = 3654 Solving for variable 'x'. Reorder the terms: 12600 + -3654 + 230x + x2 = 3654 + -3654 Combine like terms: 12600 + -3654 = 8946 8946 + 230x + x2 = 3654 + -3654 Combine like terms: 3654 + -3654 = 0 8946 + 230x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8946' to each side of the equation. 8946 + 230x + -8946 + x2 = 0 + -8946 Reorder the terms: 8946 + -8946 + 230x + x2 = 0 + -8946 Combine like terms: 8946 + -8946 = 0 0 + 230x + x2 = 0 + -8946 230x + x2 = 0 + -8946 Combine like terms: 0 + -8946 = -8946 230x + x2 = -8946 The x term is 230x. Take half its coefficient (115). Square it (13225) and add it to both sides. Add '13225' to each side of the equation. 230x + 13225 + x2 = -8946 + 13225 Reorder the terms: 13225 + 230x + x2 = -8946 + 13225 Combine like terms: -8946 + 13225 = 4279 13225 + 230x + x2 = 4279 Factor a perfect square on the left side: (x + 115)(x + 115) = 4279 Calculate the square root of the right side: 65.414065766 Break this problem into two subproblems by setting (x + 115) equal to 65.414065766 and -65.414065766.Subproblem 1
x + 115 = 65.414065766 Simplifying x + 115 = 65.414065766 Reorder the terms: 115 + x = 65.414065766 Solving 115 + x = 65.414065766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-115' to each side of the equation. 115 + -115 + x = 65.414065766 + -115 Combine like terms: 115 + -115 = 0 0 + x = 65.414065766 + -115 x = 65.414065766 + -115 Combine like terms: 65.414065766 + -115 = -49.585934234 x = -49.585934234 Simplifying x = -49.585934234Subproblem 2
x + 115 = -65.414065766 Simplifying x + 115 = -65.414065766 Reorder the terms: 115 + x = -65.414065766 Solving 115 + x = -65.414065766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-115' to each side of the equation. 115 + -115 + x = -65.414065766 + -115 Combine like terms: 115 + -115 = 0 0 + x = -65.414065766 + -115 x = -65.414065766 + -115 Combine like terms: -65.414065766 + -115 = -180.414065766 x = -180.414065766 Simplifying x = -180.414065766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-49.585934234, -180.414065766}
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