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Simplifying 120x + 0.2x2 = 12000 Solving 120x + 0.2x2 = 12000 Solving for variable 'x'. Reorder the terms: -12000 + 120x + 0.2x2 = 12000 + -12000 Combine like terms: 12000 + -12000 = 0 -12000 + 120x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -60000 + 600x + x2 = 0 Move the constant term to the right: Add '60000' to each side of the equation. -60000 + 600x + 60000 + x2 = 0 + 60000 Reorder the terms: -60000 + 60000 + 600x + x2 = 0 + 60000 Combine like terms: -60000 + 60000 = 0 0 + 600x + x2 = 0 + 60000 600x + x2 = 0 + 60000 Combine like terms: 0 + 60000 = 60000 600x + x2 = 60000 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 60000 + 90000 Reorder the terms: 90000 + 600x + x2 = 60000 + 90000 Combine like terms: 60000 + 90000 = 150000 90000 + 600x + x2 = 150000 Factor a perfect square on the left side: (x + 300)(x + 300) = 150000 Calculate the square root of the right side: 387.298334621 Break this problem into two subproblems by setting (x + 300) equal to 387.298334621 and -387.298334621.Subproblem 1
x + 300 = 387.298334621 Simplifying x + 300 = 387.298334621 Reorder the terms: 300 + x = 387.298334621 Solving 300 + x = 387.298334621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 387.298334621 + -300 Combine like terms: 300 + -300 = 0 0 + x = 387.298334621 + -300 x = 387.298334621 + -300 Combine like terms: 387.298334621 + -300 = 87.298334621 x = 87.298334621 Simplifying x = 87.298334621Subproblem 2
x + 300 = -387.298334621 Simplifying x + 300 = -387.298334621 Reorder the terms: 300 + x = -387.298334621 Solving 300 + x = -387.298334621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -387.298334621 + -300 Combine like terms: 300 + -300 = 0 0 + x = -387.298334621 + -300 x = -387.298334621 + -300 Combine like terms: -387.298334621 + -300 = -687.298334621 x = -687.298334621 Simplifying x = -687.298334621Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.298334621, -687.298334621}
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