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Simplifying x = -0.4x2 + 80x + -1600 Reorder the terms: x = -1600 + 80x + -0.4x2 Solving x = -1600 + 80x + -0.4x2 Solving for variable 'x'. Reorder the terms: 1600 + x + -80x + 0.4x2 = -1600 + 80x + -0.4x2 + 1600 + -80x + 0.4x2 Combine like terms: x + -80x = -79x 1600 + -79x + 0.4x2 = -1600 + 80x + -0.4x2 + 1600 + -80x + 0.4x2 Reorder the terms: 1600 + -79x + 0.4x2 = -1600 + 1600 + 80x + -80x + -0.4x2 + 0.4x2 Combine like terms: -1600 + 1600 = 0 1600 + -79x + 0.4x2 = 0 + 80x + -80x + -0.4x2 + 0.4x2 1600 + -79x + 0.4x2 = 80x + -80x + -0.4x2 + 0.4x2 Combine like terms: 80x + -80x = 0 1600 + -79x + 0.4x2 = 0 + -0.4x2 + 0.4x2 1600 + -79x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 1600 + -79x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 4000 + -197.5x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -197.5x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -197.5x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -197.5x + x2 = 0 + -4000 -197.5x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -197.5x + x2 = -4000 The x term is -197.5x. Take half its coefficient (-98.75). Square it (9751.5625) and add it to both sides. Add '9751.5625' to each side of the equation. -197.5x + 9751.5625 + x2 = -4000 + 9751.5625 Reorder the terms: 9751.5625 + -197.5x + x2 = -4000 + 9751.5625 Combine like terms: -4000 + 9751.5625 = 5751.5625 9751.5625 + -197.5x + x2 = 5751.5625 Factor a perfect square on the left side: (x + -98.75)(x + -98.75) = 5751.5625 Calculate the square root of the right side: 75.839056561 Break this problem into two subproblems by setting (x + -98.75) equal to 75.839056561 and -75.839056561.Subproblem 1
x + -98.75 = 75.839056561 Simplifying x + -98.75 = 75.839056561 Reorder the terms: -98.75 + x = 75.839056561 Solving -98.75 + x = 75.839056561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.75' to each side of the equation. -98.75 + 98.75 + x = 75.839056561 + 98.75 Combine like terms: -98.75 + 98.75 = 0.00 0.00 + x = 75.839056561 + 98.75 x = 75.839056561 + 98.75 Combine like terms: 75.839056561 + 98.75 = 174.589056561 x = 174.589056561 Simplifying x = 174.589056561Subproblem 2
x + -98.75 = -75.839056561 Simplifying x + -98.75 = -75.839056561 Reorder the terms: -98.75 + x = -75.839056561 Solving -98.75 + x = -75.839056561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.75' to each side of the equation. -98.75 + 98.75 + x = -75.839056561 + 98.75 Combine like terms: -98.75 + 98.75 = 0.00 0.00 + x = -75.839056561 + 98.75 x = -75.839056561 + 98.75 Combine like terms: -75.839056561 + 98.75 = 22.910943439 x = 22.910943439 Simplifying x = 22.910943439Solution
The solution to the problem is based on the solutions from the subproblems. x = {174.589056561, 22.910943439}
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