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Simplifying 3000x2 + 2500x + -6021 = 0 Reorder the terms: -6021 + 2500x + 3000x2 = 0 Solving -6021 + 2500x + 3000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3000 the coefficient of the squared term: Divide each side by '3000'. -2.007 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '2.007' to each side of the equation. -2.007 + 0.8333333333x + 2.007 + x2 = 0 + 2.007 Reorder the terms: -2.007 + 2.007 + 0.8333333333x + x2 = 0 + 2.007 Combine like terms: -2.007 + 2.007 = 0.000 0.000 + 0.8333333333x + x2 = 0 + 2.007 0.8333333333x + x2 = 0 + 2.007 Combine like terms: 0 + 2.007 = 2.007 0.8333333333x + x2 = 2.007 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 2.007 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 2.007 + 0.1736111111 Combine like terms: 2.007 + 0.1736111111 = 2.1806111111 0.1736111111 + 0.8333333333x + x2 = 2.1806111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 2.1806111111 Calculate the square root of the right side: 1.47668924 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.47668924 and -1.47668924.Subproblem 1
x + 0.4166666667 = 1.47668924 Simplifying x + 0.4166666667 = 1.47668924 Reorder the terms: 0.4166666667 + x = 1.47668924 Solving 0.4166666667 + x = 1.47668924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 1.47668924 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.47668924 + -0.4166666667 x = 1.47668924 + -0.4166666667 Combine like terms: 1.47668924 + -0.4166666667 = 1.0600225733 x = 1.0600225733 Simplifying x = 1.0600225733Subproblem 2
x + 0.4166666667 = -1.47668924 Simplifying x + 0.4166666667 = -1.47668924 Reorder the terms: 0.4166666667 + x = -1.47668924 Solving 0.4166666667 + x = -1.47668924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -1.47668924 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.47668924 + -0.4166666667 x = -1.47668924 + -0.4166666667 Combine like terms: -1.47668924 + -0.4166666667 = -1.8933559067 x = -1.8933559067 Simplifying x = -1.8933559067Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0600225733, -1.8933559067}
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