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Simplifying 0.04x2 + -9x + -6000 = 0 Reorder the terms: -6000 + -9x + 0.04x2 = 0 Solving -6000 + -9x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -150000 + -225x + x2 = 0 Move the constant term to the right: Add '150000' to each side of the equation. -150000 + -225x + 150000 + x2 = 0 + 150000 Reorder the terms: -150000 + 150000 + -225x + x2 = 0 + 150000 Combine like terms: -150000 + 150000 = 0 0 + -225x + x2 = 0 + 150000 -225x + x2 = 0 + 150000 Combine like terms: 0 + 150000 = 150000 -225x + x2 = 150000 The x term is -225x. Take half its coefficient (-112.5). Square it (12656.25) and add it to both sides. Add '12656.25' to each side of the equation. -225x + 12656.25 + x2 = 150000 + 12656.25 Reorder the terms: 12656.25 + -225x + x2 = 150000 + 12656.25 Combine like terms: 150000 + 12656.25 = 162656.25 12656.25 + -225x + x2 = 162656.25 Factor a perfect square on the left side: (x + -112.5)(x + -112.5) = 162656.25 Calculate the square root of the right side: 403.306645123 Break this problem into two subproblems by setting (x + -112.5) equal to 403.306645123 and -403.306645123.Subproblem 1
x + -112.5 = 403.306645123 Simplifying x + -112.5 = 403.306645123 Reorder the terms: -112.5 + x = 403.306645123 Solving -112.5 + x = 403.306645123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112.5' to each side of the equation. -112.5 + 112.5 + x = 403.306645123 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + x = 403.306645123 + 112.5 x = 403.306645123 + 112.5 Combine like terms: 403.306645123 + 112.5 = 515.806645123 x = 515.806645123 Simplifying x = 515.806645123Subproblem 2
x + -112.5 = -403.306645123 Simplifying x + -112.5 = -403.306645123 Reorder the terms: -112.5 + x = -403.306645123 Solving -112.5 + x = -403.306645123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112.5' to each side of the equation. -112.5 + 112.5 + x = -403.306645123 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + x = -403.306645123 + 112.5 x = -403.306645123 + 112.5 Combine like terms: -403.306645123 + 112.5 = -290.806645123 x = -290.806645123 Simplifying x = -290.806645123Solution
The solution to the problem is based on the solutions from the subproblems. x = {515.806645123, -290.806645123}
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