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Simplifying x2 + 314.011706x = 24672.00111525761 Reorder the terms: 314.011706x + x2 = 24672.00111525761 Solving 314.011706x + x2 = 24672.00111525761 Solving for variable 'x'. Reorder the terms: -24672.00111525761 + 314.011706x + x2 = 24672.00111525761 + -24672.00111525761 Combine like terms: 24672.00111525761 + -24672.00111525761 = 0.00000000000 -24672.00111525761 + 314.011706x + x2 = 0.00000000000 Begin completing the square. Move the constant term to the right: Add '24672.00111525761' to each side of the equation. -24672.00111525761 + 314.011706x + 24672.00111525761 + x2 = 0.00000000000 + 24672.00111525761 Reorder the terms: -24672.00111525761 + 24672.00111525761 + 314.011706x + x2 = 0.00000000000 + 24672.00111525761 Combine like terms: -24672.00111525761 + 24672.00111525761 = 0.00000000000 0.00000000000 + 314.011706x + x2 = 0.00000000000 + 24672.00111525761 314.011706x + x2 = 0.00000000000 + 24672.00111525761 Combine like terms: 0.00000000000 + 24672.00111525761 = 24672.00111525761 314.011706x + x2 = 24672.00111525761 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 = 24672.00111525761 + 24650.83788 Reorder the terms: 24650.83788 + 314.011706x + x2 = 24672.00111525761 + 24650.83788 Combine like terms: 24672.00111525761 + 24650.83788 = 49322.83899525761 24650.83788 + 314.011706x + x2 = 49322.83899525761 Factor a perfect square on the left side: (x + 157.005853)(x + 157.005853) = 49322.83899525761 Calculate the square root of the right side: 222.087457987 Break this problem into two subproblems by setting (x + 157.005853) equal to 222.087457987 and -222.087457987.Subproblem 1
x + 157.005853 = 222.087457987 Simplifying x + 157.005853 = 222.087457987 Reorder the terms: 157.005853 + x = 222.087457987 Solving 157.005853 + x = 222.087457987 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 = 222.087457987 + -157.005853 Combine like terms: 157.005853 + -157.005853 = 0.000000 0.000000 + x = 222.087457987 + -157.005853 x = 222.087457987 + -157.005853 Combine like terms: 222.087457987 + -157.005853 = 65.081604987 x = 65.081604987 Simplifying x = 65.081604987Subproblem 2
x + 157.005853 = -222.087457987 Simplifying x + 157.005853 = -222.087457987 Reorder the terms: 157.005853 + x = -222.087457987 Solving 157.005853 + x = -222.087457987 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 = -222.087457987 + -157.005853 Combine like terms: 157.005853 + -157.005853 = 0.000000 0.000000 + x = -222.087457987 + -157.005853 x = -222.087457987 + -157.005853 Combine like terms: -222.087457987 + -157.005853 = -379.093310987 x = -379.093310987 Simplifying x = -379.093310987Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.081604987, -379.093310987}
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