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Simplifying 0.003x2 + -35x + -42 = 0 Reorder the terms: -42 + -35x + 0.003x2 = 0 Solving -42 + -35x + 0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. -14000 + -11666.66667x + x2 = 0 Move the constant term to the right: Add '14000' to each side of the equation. -14000 + -11666.66667x + 14000 + x2 = 0 + 14000 Reorder the terms: -14000 + 14000 + -11666.66667x + x2 = 0 + 14000 Combine like terms: -14000 + 14000 = 0 0 + -11666.66667x + x2 = 0 + 14000 -11666.66667x + x2 = 0 + 14000 Combine like terms: 0 + 14000 = 14000 -11666.66667x + x2 = 14000 The x term is -11666.66667x. Take half its coefficient (-5833.333335). Square it (34027777.80) and add it to both sides. Add '34027777.80' to each side of the equation. -11666.66667x + 34027777.80 + x2 = 14000 + 34027777.80 Reorder the terms: 34027777.80 + -11666.66667x + x2 = 14000 + 34027777.80 Combine like terms: 14000 + 34027777.80 = 34041777.8 34027777.80 + -11666.66667x + x2 = 34041777.8 Factor a perfect square on the left side: (x + -5833.333335)(x + -5833.333335) = 34041777.8 Calculate the square root of the right side: 5834.533211835 Break this problem into two subproblems by setting (x + -5833.333335) equal to 5834.533211835 and -5834.533211835.Subproblem 1
x + -5833.333335 = 5834.533211835 Simplifying x + -5833.333335 = 5834.533211835 Reorder the terms: -5833.333335 + x = 5834.533211835 Solving -5833.333335 + x = 5834.533211835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5833.333335' to each side of the equation. -5833.333335 + 5833.333335 + x = 5834.533211835 + 5833.333335 Combine like terms: -5833.333335 + 5833.333335 = 0.000000 0.000000 + x = 5834.533211835 + 5833.333335 x = 5834.533211835 + 5833.333335 Combine like terms: 5834.533211835 + 5833.333335 = 11667.866546835 x = 11667.866546835 Simplifying x = 11667.866546835Subproblem 2
x + -5833.333335 = -5834.533211835 Simplifying x + -5833.333335 = -5834.533211835 Reorder the terms: -5833.333335 + x = -5834.533211835 Solving -5833.333335 + x = -5834.533211835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5833.333335' to each side of the equation. -5833.333335 + 5833.333335 + x = -5834.533211835 + 5833.333335 Combine like terms: -5833.333335 + 5833.333335 = 0.000000 0.000000 + x = -5834.533211835 + 5833.333335 x = -5834.533211835 + 5833.333335 Combine like terms: -5834.533211835 + 5833.333335 = -1.199876835 x = -1.199876835 Simplifying x = -1.199876835Solution
The solution to the problem is based on the solutions from the subproblems. x = {11667.866546835, -1.199876835}
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