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Simplifying 1.5x2 + -900x + 5000 = 0 Reorder the terms: 5000 + -900x + 1.5x2 = 0 Solving 5000 + -900x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 3333.333333 + -600x + x2 = 0 Move the constant term to the right: Add '-3333.333333' to each side of the equation. 3333.333333 + -600x + -3333.333333 + x2 = 0 + -3333.333333 Reorder the terms: 3333.333333 + -3333.333333 + -600x + x2 = 0 + -3333.333333 Combine like terms: 3333.333333 + -3333.333333 = 0.000000 0.000000 + -600x + x2 = 0 + -3333.333333 -600x + x2 = 0 + -3333.333333 Combine like terms: 0 + -3333.333333 = -3333.333333 -600x + x2 = -3333.333333 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -3333.333333 + 90000 Reorder the terms: 90000 + -600x + x2 = -3333.333333 + 90000 Combine like terms: -3333.333333 + 90000 = 86666.666667 90000 + -600x + x2 = 86666.666667 Factor a perfect square on the left side: (x + -300)(x + -300) = 86666.666667 Calculate the square root of the right side: 294.392028878 Break this problem into two subproblems by setting (x + -300) equal to 294.392028878 and -294.392028878.Subproblem 1
x + -300 = 294.392028878 Simplifying x + -300 = 294.392028878 Reorder the terms: -300 + x = 294.392028878 Solving -300 + x = 294.392028878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 294.392028878 + 300 Combine like terms: -300 + 300 = 0 0 + x = 294.392028878 + 300 x = 294.392028878 + 300 Combine like terms: 294.392028878 + 300 = 594.392028878 x = 594.392028878 Simplifying x = 594.392028878Subproblem 2
x + -300 = -294.392028878 Simplifying x + -300 = -294.392028878 Reorder the terms: -300 + x = -294.392028878 Solving -300 + x = -294.392028878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -294.392028878 + 300 Combine like terms: -300 + 300 = 0 0 + x = -294.392028878 + 300 x = -294.392028878 + 300 Combine like terms: -294.392028878 + 300 = 5.607971122 x = 5.607971122 Simplifying x = 5.607971122Solution
The solution to the problem is based on the solutions from the subproblems. x = {594.392028878, 5.607971122}
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