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Simplifying 40000000 = 0.012x2 + -0.573x + 35.724 Reorder the terms: 40000000 = 35.724 + -0.573x + 0.012x2 Solving 40000000 = 35.724 + -0.573x + 0.012x2 Solving for variable 'x'. Combine like terms: 40000000 + -35.724 = 39999964.276 39999964.276 + 0.573x + -0.012x2 = 35.724 + -0.573x + 0.012x2 + -35.724 + 0.573x + -0.012x2 Reorder the terms: 39999964.276 + 0.573x + -0.012x2 = 35.724 + -35.724 + -0.573x + 0.573x + 0.012x2 + -0.012x2 Combine like terms: 35.724 + -35.724 = 0.000 39999964.276 + 0.573x + -0.012x2 = 0.000 + -0.573x + 0.573x + 0.012x2 + -0.012x2 39999964.276 + 0.573x + -0.012x2 = -0.573x + 0.573x + 0.012x2 + -0.012x2 Combine like terms: -0.573x + 0.573x = 0.000 39999964.276 + 0.573x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 39999964.276 + 0.573x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 39999964.276 + 0.573x + -0.012x2 = 0.000 Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -3333330356 + -47.75x + x2 = 0 Move the constant term to the right: Add '3333330356' to each side of the equation. -3333330356 + -47.75x + 3333330356 + x2 = 0 + 3333330356 Reorder the terms: -3333330356 + 3333330356 + -47.75x + x2 = 0 + 3333330356 Combine like terms: -3333330356 + 3333330356 = 0 0 + -47.75x + x2 = 0 + 3333330356 -47.75x + x2 = 0 + 3333330356 Combine like terms: 0 + 3333330356 = 3333330356 -47.75x + x2 = 3333330356 The x term is -47.75x. Take half its coefficient (-23.875). Square it (570.015625) and add it to both sides. Add '570.015625' to each side of the equation. -47.75x + 570.015625 + x2 = 3333330356 + 570.015625 Reorder the terms: 570.015625 + -47.75x + x2 = 3333330356 + 570.015625 Combine like terms: 3333330356 + 570.015625 = 3333330926.015625 570.015625 + -47.75x + x2 = 3333330926.015625 Factor a perfect square on the left side: (x + -23.875)(x + -23.875) = 3333330926.015625 Calculate the square root of the right side: 57735.006070976 Break this problem into two subproblems by setting (x + -23.875) equal to 57735.006070976 and -57735.006070976.Subproblem 1
x + -23.875 = 57735.006070976 Simplifying x + -23.875 = 57735.006070976 Reorder the terms: -23.875 + x = 57735.006070976 Solving -23.875 + x = 57735.006070976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = 57735.006070976 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = 57735.006070976 + 23.875 x = 57735.006070976 + 23.875 Combine like terms: 57735.006070976 + 23.875 = 57758.881070976 x = 57758.881070976 Simplifying x = 57758.881070976Subproblem 2
x + -23.875 = -57735.006070976 Simplifying x + -23.875 = -57735.006070976 Reorder the terms: -23.875 + x = -57735.006070976 Solving -23.875 + x = -57735.006070976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = -57735.006070976 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = -57735.006070976 + 23.875 x = -57735.006070976 + 23.875 Combine like terms: -57735.006070976 + 23.875 = -57711.131070976 x = -57711.131070976 Simplifying x = -57711.131070976Solution
The solution to the problem is based on the solutions from the subproblems. x = {57758.881070976, -57711.131070976}
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