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Simplifying -0.032x2 + 46x + -3000 = 0 Reorder the terms: -3000 + 46x + -0.032x2 = 0 Solving -3000 + 46x + -0.032x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.032 the coefficient of the squared term: Divide each side by '-0.032'. 93750 + -1437.5x + x2 = 0 Move the constant term to the right: Add '-93750' to each side of the equation. 93750 + -1437.5x + -93750 + x2 = 0 + -93750 Reorder the terms: 93750 + -93750 + -1437.5x + x2 = 0 + -93750 Combine like terms: 93750 + -93750 = 0 0 + -1437.5x + x2 = 0 + -93750 -1437.5x + x2 = 0 + -93750 Combine like terms: 0 + -93750 = -93750 -1437.5x + x2 = -93750 The x term is -1437.5x. Take half its coefficient (-718.75). Square it (516601.5625) and add it to both sides. Add '516601.5625' to each side of the equation. -1437.5x + 516601.5625 + x2 = -93750 + 516601.5625 Reorder the terms: 516601.5625 + -1437.5x + x2 = -93750 + 516601.5625 Combine like terms: -93750 + 516601.5625 = 422851.5625 516601.5625 + -1437.5x + x2 = 422851.5625 Factor a perfect square on the left side: (x + -718.75)(x + -718.75) = 422851.5625 Calculate the square root of the right side: 650.270376459 Break this problem into two subproblems by setting (x + -718.75) equal to 650.270376459 and -650.270376459.Subproblem 1
x + -718.75 = 650.270376459 Simplifying x + -718.75 = 650.270376459 Reorder the terms: -718.75 + x = 650.270376459 Solving -718.75 + x = 650.270376459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '718.75' to each side of the equation. -718.75 + 718.75 + x = 650.270376459 + 718.75 Combine like terms: -718.75 + 718.75 = 0.00 0.00 + x = 650.270376459 + 718.75 x = 650.270376459 + 718.75 Combine like terms: 650.270376459 + 718.75 = 1369.020376459 x = 1369.020376459 Simplifying x = 1369.020376459Subproblem 2
x + -718.75 = -650.270376459 Simplifying x + -718.75 = -650.270376459 Reorder the terms: -718.75 + x = -650.270376459 Solving -718.75 + x = -650.270376459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '718.75' to each side of the equation. -718.75 + 718.75 + x = -650.270376459 + 718.75 Combine like terms: -718.75 + 718.75 = 0.00 0.00 + x = -650.270376459 + 718.75 x = -650.270376459 + 718.75 Combine like terms: -650.270376459 + 718.75 = 68.479623541 x = 68.479623541 Simplifying x = 68.479623541Solution
The solution to the problem is based on the solutions from the subproblems. x = {1369.020376459, 68.479623541}
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