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Simplifying 50000000 = 0.012x2 + -0.543x + 35.727 Reorder the terms: 50000000 = 35.727 + -0.543x + 0.012x2 Solving 50000000 = 35.727 + -0.543x + 0.012x2 Solving for variable 'x'. Combine like terms: 50000000 + -35.727 = 49999964.273 49999964.273 + 0.543x + -0.012x2 = 35.727 + -0.543x + 0.012x2 + -35.727 + 0.543x + -0.012x2 Reorder the terms: 49999964.273 + 0.543x + -0.012x2 = 35.727 + -35.727 + -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: 35.727 + -35.727 = 0.000 49999964.273 + 0.543x + -0.012x2 = 0.000 + -0.543x + 0.543x + 0.012x2 + -0.012x2 49999964.273 + 0.543x + -0.012x2 = -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: -0.543x + 0.543x = 0.000 49999964.273 + 0.543x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 49999964.273 + 0.543x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 49999964.273 + 0.543x + -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'. -4166663689 + -45.25x + x2 = 0 Move the constant term to the right: Add '4166663689' to each side of the equation. -4166663689 + -45.25x + 4166663689 + x2 = 0 + 4166663689 Reorder the terms: -4166663689 + 4166663689 + -45.25x + x2 = 0 + 4166663689 Combine like terms: -4166663689 + 4166663689 = 0 0 + -45.25x + x2 = 0 + 4166663689 -45.25x + x2 = 0 + 4166663689 Combine like terms: 0 + 4166663689 = 4166663689 -45.25x + x2 = 4166663689 The x term is -45.25x. Take half its coefficient (-22.625). Square it (511.890625) and add it to both sides. Add '511.890625' to each side of the equation. -45.25x + 511.890625 + x2 = 4166663689 + 511.890625 Reorder the terms: 511.890625 + -45.25x + x2 = 4166663689 + 511.890625 Combine like terms: 4166663689 + 511.890625 = 4166664200.890625 511.890625 + -45.25x + x2 = 4166664200.890625 Factor a perfect square on the left side: (x + -22.625)(x + -22.625) = 4166664200.890625 Calculate the square root of the right side: 64549.703336968 Break this problem into two subproblems by setting (x + -22.625) equal to 64549.703336968 and -64549.703336968.Subproblem 1
x + -22.625 = 64549.703336968 Simplifying x + -22.625 = 64549.703336968 Reorder the terms: -22.625 + x = 64549.703336968 Solving -22.625 + x = 64549.703336968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = 64549.703336968 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = 64549.703336968 + 22.625 x = 64549.703336968 + 22.625 Combine like terms: 64549.703336968 + 22.625 = 64572.328336968 x = 64572.328336968 Simplifying x = 64572.328336968Subproblem 2
x + -22.625 = -64549.703336968 Simplifying x + -22.625 = -64549.703336968 Reorder the terms: -22.625 + x = -64549.703336968 Solving -22.625 + x = -64549.703336968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = -64549.703336968 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = -64549.703336968 + 22.625 x = -64549.703336968 + 22.625 Combine like terms: -64549.703336968 + 22.625 = -64527.078336968 x = -64527.078336968 Simplifying x = -64527.078336968Solution
The solution to the problem is based on the solutions from the subproblems. x = {64572.328336968, -64527.078336968}
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