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Simplifying 39x2 + -476x + -2459 = 0 Reorder the terms: -2459 + -476x + 39x2 = 0 Solving -2459 + -476x + 39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -63.05128205 + -12.20512821x + x2 = 0 Move the constant term to the right: Add '63.05128205' to each side of the equation. -63.05128205 + -12.20512821x + 63.05128205 + x2 = 0 + 63.05128205 Reorder the terms: -63.05128205 + 63.05128205 + -12.20512821x + x2 = 0 + 63.05128205 Combine like terms: -63.05128205 + 63.05128205 = 0.00000000 0.00000000 + -12.20512821x + x2 = 0 + 63.05128205 -12.20512821x + x2 = 0 + 63.05128205 Combine like terms: 0 + 63.05128205 = 63.05128205 -12.20512821x + x2 = 63.05128205 The x term is -12.20512821x. Take half its coefficient (-6.102564105). Square it (37.24128866) and add it to both sides. Add '37.24128866' to each side of the equation. -12.20512821x + 37.24128866 + x2 = 63.05128205 + 37.24128866 Reorder the terms: 37.24128866 + -12.20512821x + x2 = 63.05128205 + 37.24128866 Combine like terms: 63.05128205 + 37.24128866 = 100.29257071 37.24128866 + -12.20512821x + x2 = 100.29257071 Factor a perfect square on the left side: (x + -6.102564105)(x + -6.102564105) = 100.29257071 Calculate the square root of the right side: 10.014617851 Break this problem into two subproblems by setting (x + -6.102564105) equal to 10.014617851 and -10.014617851.Subproblem 1
x + -6.102564105 = 10.014617851 Simplifying x + -6.102564105 = 10.014617851 Reorder the terms: -6.102564105 + x = 10.014617851 Solving -6.102564105 + x = 10.014617851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.102564105' to each side of the equation. -6.102564105 + 6.102564105 + x = 10.014617851 + 6.102564105 Combine like terms: -6.102564105 + 6.102564105 = 0.000000000 0.000000000 + x = 10.014617851 + 6.102564105 x = 10.014617851 + 6.102564105 Combine like terms: 10.014617851 + 6.102564105 = 16.117181956 x = 16.117181956 Simplifying x = 16.117181956Subproblem 2
x + -6.102564105 = -10.014617851 Simplifying x + -6.102564105 = -10.014617851 Reorder the terms: -6.102564105 + x = -10.014617851 Solving -6.102564105 + x = -10.014617851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.102564105' to each side of the equation. -6.102564105 + 6.102564105 + x = -10.014617851 + 6.102564105 Combine like terms: -6.102564105 + 6.102564105 = 0.000000000 0.000000000 + x = -10.014617851 + 6.102564105 x = -10.014617851 + 6.102564105 Combine like terms: -10.014617851 + 6.102564105 = -3.912053746 x = -3.912053746 Simplifying x = -3.912053746Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.117181956, -3.912053746}
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