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Simplifying 3x2 + -5x + -3000 = 0 Reorder the terms: -3000 + -5x + 3x2 = 0 Solving -3000 + -5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1000 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -1.666666667x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -1.666666667x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -1.666666667x + x2 = 0 + 1000 -1.666666667x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -1.666666667x + x2 = 1000 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1000 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1000 + 0.6944444447 Combine like terms: 1000 + 0.6944444447 = 1000.6944444447 0.6944444447 + -1.666666667x + x2 = 1000.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1000.6944444447 Calculate the square root of the right side: 31.633754827 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 31.633754827 and -31.633754827.Subproblem 1
x + -0.8333333335 = 31.633754827 Simplifying x + -0.8333333335 = 31.633754827 Reorder the terms: -0.8333333335 + x = 31.633754827 Solving -0.8333333335 + x = 31.633754827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 31.633754827 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 31.633754827 + 0.8333333335 x = 31.633754827 + 0.8333333335 Combine like terms: 31.633754827 + 0.8333333335 = 32.4670881605 x = 32.4670881605 Simplifying x = 32.4670881605Subproblem 2
x + -0.8333333335 = -31.633754827 Simplifying x + -0.8333333335 = -31.633754827 Reorder the terms: -0.8333333335 + x = -31.633754827 Solving -0.8333333335 + x = -31.633754827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -31.633754827 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -31.633754827 + 0.8333333335 x = -31.633754827 + 0.8333333335 Combine like terms: -31.633754827 + 0.8333333335 = -30.8004214935 x = -30.8004214935 Simplifying x = -30.8004214935Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.4670881605, -30.8004214935}
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