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Simplifying (x + 80)(x + 20) = 16500 Reorder the terms: (80 + x)(x + 20) = 16500 Reorder the terms: (80 + x)(20 + x) = 16500 Multiply (80 + x) * (20 + x) (80(20 + x) + x(20 + x)) = 16500 ((20 * 80 + x * 80) + x(20 + x)) = 16500 ((1600 + 80x) + x(20 + x)) = 16500 (1600 + 80x + (20 * x + x * x)) = 16500 (1600 + 80x + (20x + x2)) = 16500 Combine like terms: 80x + 20x = 100x (1600 + 100x + x2) = 16500 Solving 1600 + 100x + x2 = 16500 Solving for variable 'x'. Reorder the terms: 1600 + -16500 + 100x + x2 = 16500 + -16500 Combine like terms: 1600 + -16500 = -14900 -14900 + 100x + x2 = 16500 + -16500 Combine like terms: 16500 + -16500 = 0 -14900 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14900' to each side of the equation. -14900 + 100x + 14900 + x2 = 0 + 14900 Reorder the terms: -14900 + 14900 + 100x + x2 = 0 + 14900 Combine like terms: -14900 + 14900 = 0 0 + 100x + x2 = 0 + 14900 100x + x2 = 0 + 14900 Combine like terms: 0 + 14900 = 14900 100x + x2 = 14900 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 14900 + 2500 Reorder the terms: 2500 + 100x + x2 = 14900 + 2500 Combine like terms: 14900 + 2500 = 17400 2500 + 100x + x2 = 17400 Factor a perfect square on the left side: (x + 50)(x + 50) = 17400 Calculate the square root of the right side: 131.909059583 Break this problem into two subproblems by setting (x + 50) equal to 131.909059583 and -131.909059583.Subproblem 1
x + 50 = 131.909059583 Simplifying x + 50 = 131.909059583 Reorder the terms: 50 + x = 131.909059583 Solving 50 + x = 131.909059583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 131.909059583 + -50 Combine like terms: 50 + -50 = 0 0 + x = 131.909059583 + -50 x = 131.909059583 + -50 Combine like terms: 131.909059583 + -50 = 81.909059583 x = 81.909059583 Simplifying x = 81.909059583Subproblem 2
x + 50 = -131.909059583 Simplifying x + 50 = -131.909059583 Reorder the terms: 50 + x = -131.909059583 Solving 50 + x = -131.909059583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -131.909059583 + -50 Combine like terms: 50 + -50 = 0 0 + x = -131.909059583 + -50 x = -131.909059583 + -50 Combine like terms: -131.909059583 + -50 = -181.909059583 x = -181.909059583 Simplifying x = -181.909059583Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.909059583, -181.909059583}
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