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Simplifying x(40 + 0.5625x) = 200 (40 * x + 0.5625x * x) = 200 (40x + 0.5625x2) = 200 Solving 40x + 0.5625x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 40x + 0.5625x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 40x + 0.5625x2 = 0 Begin completing the square. Divide all terms by 0.5625 the coefficient of the squared term: Divide each side by '0.5625'. -355.5555556 + 71.11111111x + x2 = 0 Move the constant term to the right: Add '355.5555556' to each side of the equation. -355.5555556 + 71.11111111x + 355.5555556 + x2 = 0 + 355.5555556 Reorder the terms: -355.5555556 + 355.5555556 + 71.11111111x + x2 = 0 + 355.5555556 Combine like terms: -355.5555556 + 355.5555556 = 0.0000000 0.0000000 + 71.11111111x + x2 = 0 + 355.5555556 71.11111111x + x2 = 0 + 355.5555556 Combine like terms: 0 + 355.5555556 = 355.5555556 71.11111111x + x2 = 355.5555556 The x term is 71.11111111x. Take half its coefficient (35.55555556). Square it (1264.197531) and add it to both sides. Add '1264.197531' to each side of the equation. 71.11111111x + 1264.197531 + x2 = 355.5555556 + 1264.197531 Reorder the terms: 1264.197531 + 71.11111111x + x2 = 355.5555556 + 1264.197531 Combine like terms: 355.5555556 + 1264.197531 = 1619.7530866 1264.197531 + 71.11111111x + x2 = 1619.7530866 Factor a perfect square on the left side: (x + 35.55555556)(x + 35.55555556) = 1619.7530866 Calculate the square root of the right side: 40.246156172 Break this problem into two subproblems by setting (x + 35.55555556) equal to 40.246156172 and -40.246156172.Subproblem 1
x + 35.55555556 = 40.246156172 Simplifying x + 35.55555556 = 40.246156172 Reorder the terms: 35.55555556 + x = 40.246156172 Solving 35.55555556 + x = 40.246156172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.55555556' to each side of the equation. 35.55555556 + -35.55555556 + x = 40.246156172 + -35.55555556 Combine like terms: 35.55555556 + -35.55555556 = 0.00000000 0.00000000 + x = 40.246156172 + -35.55555556 x = 40.246156172 + -35.55555556 Combine like terms: 40.246156172 + -35.55555556 = 4.690600612 x = 4.690600612 Simplifying x = 4.690600612Subproblem 2
x + 35.55555556 = -40.246156172 Simplifying x + 35.55555556 = -40.246156172 Reorder the terms: 35.55555556 + x = -40.246156172 Solving 35.55555556 + x = -40.246156172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.55555556' to each side of the equation. 35.55555556 + -35.55555556 + x = -40.246156172 + -35.55555556 Combine like terms: 35.55555556 + -35.55555556 = 0.00000000 0.00000000 + x = -40.246156172 + -35.55555556 x = -40.246156172 + -35.55555556 Combine like terms: -40.246156172 + -35.55555556 = -75.801711732 x = -75.801711732 Simplifying x = -75.801711732Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.690600612, -75.801711732}
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