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Simplifying 0.36x2 + -7x + -6000 = 0 Reorder the terms: -6000 + -7x + 0.36x2 = 0 Solving -6000 + -7x + 0.36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. -16666.66667 + -19.44444444x + x2 = 0 Move the constant term to the right: Add '16666.66667' to each side of the equation. -16666.66667 + -19.44444444x + 16666.66667 + x2 = 0 + 16666.66667 Reorder the terms: -16666.66667 + 16666.66667 + -19.44444444x + x2 = 0 + 16666.66667 Combine like terms: -16666.66667 + 16666.66667 = 0.00000 0.00000 + -19.44444444x + x2 = 0 + 16666.66667 -19.44444444x + x2 = 0 + 16666.66667 Combine like terms: 0 + 16666.66667 = 16666.66667 -19.44444444x + x2 = 16666.66667 The x term is -19.44444444x. Take half its coefficient (-9.72222222). Square it (94.52160490) and add it to both sides. Add '94.52160490' to each side of the equation. -19.44444444x + 94.52160490 + x2 = 16666.66667 + 94.52160490 Reorder the terms: 94.52160490 + -19.44444444x + x2 = 16666.66667 + 94.52160490 Combine like terms: 16666.66667 + 94.52160490 = 16761.1882749 94.52160490 + -19.44444444x + x2 = 16761.1882749 Factor a perfect square on the left side: (x + -9.72222222)(x + -9.72222222) = 16761.1882749 Calculate the square root of the right side: 129.465007917 Break this problem into two subproblems by setting (x + -9.72222222) equal to 129.465007917 and -129.465007917.Subproblem 1
x + -9.72222222 = 129.465007917 Simplifying x + -9.72222222 = 129.465007917 Reorder the terms: -9.72222222 + x = 129.465007917 Solving -9.72222222 + x = 129.465007917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.72222222' to each side of the equation. -9.72222222 + 9.72222222 + x = 129.465007917 + 9.72222222 Combine like terms: -9.72222222 + 9.72222222 = 0.00000000 0.00000000 + x = 129.465007917 + 9.72222222 x = 129.465007917 + 9.72222222 Combine like terms: 129.465007917 + 9.72222222 = 139.187230137 x = 139.187230137 Simplifying x = 139.187230137Subproblem 2
x + -9.72222222 = -129.465007917 Simplifying x + -9.72222222 = -129.465007917 Reorder the terms: -9.72222222 + x = -129.465007917 Solving -9.72222222 + x = -129.465007917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.72222222' to each side of the equation. -9.72222222 + 9.72222222 + x = -129.465007917 + 9.72222222 Combine like terms: -9.72222222 + 9.72222222 = 0.00000000 0.00000000 + x = -129.465007917 + 9.72222222 x = -129.465007917 + 9.72222222 Combine like terms: -129.465007917 + 9.72222222 = -119.742785697 x = -119.742785697 Simplifying x = -119.742785697Solution
The solution to the problem is based on the solutions from the subproblems. x = {139.187230137, -119.742785697}
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