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Simplifying -1x2 + 314.011706x + 24672.00111525761 = 0 Reorder the terms: 24672.00111525761 + 314.011706x + -1x2 = 0 Solving 24672.00111525761 + 314.011706x + -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'. -24672.00112 + -314.011706x + x2 = 0 Move the constant term to the right: Add '24672.00112' to each side of the equation. -24672.00112 + -314.011706x + 24672.00112 + x2 = 0 + 24672.00112 Reorder the terms: -24672.00112 + 24672.00112 + -314.011706x + x2 = 0 + 24672.00112 Combine like terms: -24672.00112 + 24672.00112 = 0.00000 0.00000 + -314.011706x + x2 = 0 + 24672.00112 -314.011706x + x2 = 0 + 24672.00112 Combine like terms: 0 + 24672.00112 = 24672.00112 -314.011706x + x2 = 24672.00112 The x term is -314.011706x. Take half its coefficient (-157.005853). Square it (24650.83788) and add it to both sides. Add '24650.83788' to each side of the equation. -314.011706x + 24650.83788 + x2 = 24672.00112 + 24650.83788 Reorder the terms: 24650.83788 + -314.011706x + x2 = 24672.00112 + 24650.83788 Combine like terms: 24672.00112 + 24650.83788 = 49322.839 24650.83788 + -314.011706x + x2 = 49322.839 Factor a perfect square on the left side: (x + -157.005853)(x + -157.005853) = 49322.839 Calculate the square root of the right side: 222.087457998 Break this problem into two subproblems by setting (x + -157.005853) equal to 222.087457998 and -222.087457998.Subproblem 1
x + -157.005853 = 222.087457998 Simplifying x + -157.005853 = 222.087457998 Reorder the terms: -157.005853 + x = 222.087457998 Solving -157.005853 + x = 222.087457998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '157.005853' to each side of the equation. -157.005853 + 157.005853 + x = 222.087457998 + 157.005853 Combine like terms: -157.005853 + 157.005853 = 0.000000 0.000000 + x = 222.087457998 + 157.005853 x = 222.087457998 + 157.005853 Combine like terms: 222.087457998 + 157.005853 = 379.093310998 x = 379.093310998 Simplifying x = 379.093310998Subproblem 2
x + -157.005853 = -222.087457998 Simplifying x + -157.005853 = -222.087457998 Reorder the terms: -157.005853 + x = -222.087457998 Solving -157.005853 + x = -222.087457998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '157.005853' to each side of the equation. -157.005853 + 157.005853 + x = -222.087457998 + 157.005853 Combine like terms: -157.005853 + 157.005853 = 0.000000 0.000000 + x = -222.087457998 + 157.005853 x = -222.087457998 + 157.005853 Combine like terms: -222.087457998 + 157.005853 = -65.081604998 x = -65.081604998 Simplifying x = -65.081604998Solution
The solution to the problem is based on the solutions from the subproblems. x = {379.093310998, -65.081604998}
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