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Simplifying 0.16x2 + -6x + -6000 = 0 Reorder the terms: -6000 + -6x + 0.16x2 = 0 Solving -6000 + -6x + 0.16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. -37500 + -37.5x + x2 = 0 Move the constant term to the right: Add '37500' to each side of the equation. -37500 + -37.5x + 37500 + x2 = 0 + 37500 Reorder the terms: -37500 + 37500 + -37.5x + x2 = 0 + 37500 Combine like terms: -37500 + 37500 = 0 0 + -37.5x + x2 = 0 + 37500 -37.5x + x2 = 0 + 37500 Combine like terms: 0 + 37500 = 37500 -37.5x + x2 = 37500 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = 37500 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = 37500 + 351.5625 Combine like terms: 37500 + 351.5625 = 37851.5625 351.5625 + -37.5x + x2 = 37851.5625 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 37851.5625 Calculate the square root of the right side: 194.554780203 Break this problem into two subproblems by setting (x + -18.75) equal to 194.554780203 and -194.554780203.Subproblem 1
x + -18.75 = 194.554780203 Simplifying x + -18.75 = 194.554780203 Reorder the terms: -18.75 + x = 194.554780203 Solving -18.75 + x = 194.554780203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 194.554780203 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 194.554780203 + 18.75 x = 194.554780203 + 18.75 Combine like terms: 194.554780203 + 18.75 = 213.304780203 x = 213.304780203 Simplifying x = 213.304780203Subproblem 2
x + -18.75 = -194.554780203 Simplifying x + -18.75 = -194.554780203 Reorder the terms: -18.75 + x = -194.554780203 Solving -18.75 + x = -194.554780203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = -194.554780203 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -194.554780203 + 18.75 x = -194.554780203 + 18.75 Combine like terms: -194.554780203 + 18.75 = -175.804780203 x = -175.804780203 Simplifying x = -175.804780203Solution
The solution to the problem is based on the solutions from the subproblems. x = {213.304780203, -175.804780203}
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