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Simplifying -314.019418x2 + 1x + 24673.20799626468 = 0 Reorder the terms: 24673.20799626468 + 1x + -314.019418x2 = 0 Solving 24673.20799626468 + 1x + -314.019418x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -314.019418 the coefficient of the squared term: Divide each side by '-314.019418'. -78.57223656 + -0.003184516443x + x2 = 0 Move the constant term to the right: Add '78.57223656' to each side of the equation. -78.57223656 + -0.003184516443x + 78.57223656 + x2 = 0 + 78.57223656 Reorder the terms: -78.57223656 + 78.57223656 + -0.003184516443x + x2 = 0 + 78.57223656 Combine like terms: -78.57223656 + 78.57223656 = 0.00000000 0.00000000 + -0.003184516443x + x2 = 0 + 78.57223656 -0.003184516443x + x2 = 0 + 78.57223656 Combine like terms: 0 + 78.57223656 = 78.57223656 -0.003184516443x + x2 = 78.57223656 The x term is -0.003184516443x. Take half its coefficient (-0.001592258222). Square it (0.000002535286246) and add it to both sides. Add '0.000002535286246' to each side of the equation. -0.003184516443x + 0.000002535286246 + x2 = 78.57223656 + 0.000002535286246 Reorder the terms: 0.000002535286246 + -0.003184516443x + x2 = 78.57223656 + 0.000002535286246 Combine like terms: 78.57223656 + 0.000002535286246 = 78.572239095286246 0.000002535286246 + -0.003184516443x + x2 = 78.572239095286246 Factor a perfect square on the left side: (x + -0.001592258222)(x + -0.001592258222) = 78.572239095286246 Calculate the square root of the right side: 8.864098324 Break this problem into two subproblems by setting (x + -0.001592258222) equal to 8.864098324 and -8.864098324.Subproblem 1
x + -0.001592258222 = 8.864098324 Simplifying x + -0.001592258222 = 8.864098324 Reorder the terms: -0.001592258222 + x = 8.864098324 Solving -0.001592258222 + x = 8.864098324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.001592258222' to each side of the equation. -0.001592258222 + 0.001592258222 + x = 8.864098324 + 0.001592258222 Combine like terms: -0.001592258222 + 0.001592258222 = 0.000000000000 0.000000000000 + x = 8.864098324 + 0.001592258222 x = 8.864098324 + 0.001592258222 Combine like terms: 8.864098324 + 0.001592258222 = 8.865690582222 x = 8.865690582222 Simplifying x = 8.865690582222Subproblem 2
x + -0.001592258222 = -8.864098324 Simplifying x + -0.001592258222 = -8.864098324 Reorder the terms: -0.001592258222 + x = -8.864098324 Solving -0.001592258222 + x = -8.864098324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.001592258222' to each side of the equation. -0.001592258222 + 0.001592258222 + x = -8.864098324 + 0.001592258222 Combine like terms: -0.001592258222 + 0.001592258222 = 0.000000000000 0.000000000000 + x = -8.864098324 + 0.001592258222 x = -8.864098324 + 0.001592258222 Combine like terms: -8.864098324 + 0.001592258222 = -8.862506065778 x = -8.862506065778 Simplifying x = -8.862506065778Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.865690582222, -8.862506065778}
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