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Simplifying -1x2 + 24672.00111525761x + 314.011706 = 0 Reorder the terms: 314.011706 + 24672.00111525761x + -1x2 = 0 Solving 314.011706 + 24672.00111525761x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -314.011706 + -24672.00112x + x2 = 0 Move the constant term to the right: Add '314.011706' to each side of the equation. -314.011706 + -24672.00112x + 314.011706 + x2 = 0 + 314.011706 Reorder the terms: -314.011706 + 314.011706 + -24672.00112x + x2 = 0 + 314.011706 Combine like terms: -314.011706 + 314.011706 = 0.000000 0.000000 + -24672.00112x + x2 = 0 + 314.011706 -24672.00112x + x2 = 0 + 314.011706 Combine like terms: 0 + 314.011706 = 314.011706 -24672.00112x + x2 = 314.011706 The x term is -24672.00112x. Take half its coefficient (-12336.00056). Square it (152176909.8) and add it to both sides. Add '152176909.8' to each side of the equation. -24672.00112x + 152176909.8 + x2 = 314.011706 + 152176909.8 Reorder the terms: 152176909.8 + -24672.00112x + x2 = 314.011706 + 152176909.8 Combine like terms: 314.011706 + 152176909.8 = 152177223.811706 152176909.8 + -24672.00112x + x2 = 152177223.811706 Factor a perfect square on the left side: (x + -12336.00056)(x + -12336.00056) = 152177223.811706 Calculate the square root of the right side: 12336.013286784 Break this problem into two subproblems by setting (x + -12336.00056) equal to 12336.013286784 and -12336.013286784.Subproblem 1
x + -12336.00056 = 12336.013286784 Simplifying x + -12336.00056 = 12336.013286784 Reorder the terms: -12336.00056 + x = 12336.013286784 Solving -12336.00056 + x = 12336.013286784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12336.00056' to each side of the equation. -12336.00056 + 12336.00056 + x = 12336.013286784 + 12336.00056 Combine like terms: -12336.00056 + 12336.00056 = 0.00000 0.00000 + x = 12336.013286784 + 12336.00056 x = 12336.013286784 + 12336.00056 Combine like terms: 12336.013286784 + 12336.00056 = 24672.013846784 x = 24672.013846784 Simplifying x = 24672.013846784Subproblem 2
x + -12336.00056 = -12336.013286784 Simplifying x + -12336.00056 = -12336.013286784 Reorder the terms: -12336.00056 + x = -12336.013286784 Solving -12336.00056 + x = -12336.013286784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12336.00056' to each side of the equation. -12336.00056 + 12336.00056 + x = -12336.013286784 + 12336.00056 Combine like terms: -12336.00056 + 12336.00056 = 0.00000 0.00000 + x = -12336.013286784 + 12336.00056 x = -12336.013286784 + 12336.00056 Combine like terms: -12336.013286784 + 12336.00056 = -0.012726784 x = -0.012726784 Simplifying x = -0.012726784Solution
The solution to the problem is based on the solutions from the subproblems. x = {24672.013846784, -0.012726784}
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