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Simplifying 39x2 + -476x + -2465 = 0 Reorder the terms: -2465 + -476x + 39x2 = 0 Solving -2465 + -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'. -63.20512821 + -12.20512821x + x2 = 0 Move the constant term to the right: Add '63.20512821' to each side of the equation. -63.20512821 + -12.20512821x + 63.20512821 + x2 = 0 + 63.20512821 Reorder the terms: -63.20512821 + 63.20512821 + -12.20512821x + x2 = 0 + 63.20512821 Combine like terms: -63.20512821 + 63.20512821 = 0.00000000 0.00000000 + -12.20512821x + x2 = 0 + 63.20512821 -12.20512821x + x2 = 0 + 63.20512821 Combine like terms: 0 + 63.20512821 = 63.20512821 -12.20512821x + x2 = 63.20512821 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 = 63.20512821 + 37.24128866 Reorder the terms: 37.24128866 + -12.20512821x + x2 = 63.20512821 + 37.24128866 Combine like terms: 63.20512821 + 37.24128866 = 100.44641687 37.24128866 + -12.20512821x + x2 = 100.44641687 Factor a perfect square on the left side: (x + -6.102564105)(x + -6.102564105) = 100.44641687 Calculate the square root of the right side: 10.022295988 Break this problem into two subproblems by setting (x + -6.102564105) equal to 10.022295988 and -10.022295988.Subproblem 1
x + -6.102564105 = 10.022295988 Simplifying x + -6.102564105 = 10.022295988 Reorder the terms: -6.102564105 + x = 10.022295988 Solving -6.102564105 + x = 10.022295988 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 = 10.022295988 + 6.102564105 Combine like terms: -6.102564105 + 6.102564105 = 0.000000000 0.000000000 + x = 10.022295988 + 6.102564105 x = 10.022295988 + 6.102564105 Combine like terms: 10.022295988 + 6.102564105 = 16.124860093 x = 16.124860093 Simplifying x = 16.124860093Subproblem 2
x + -6.102564105 = -10.022295988 Simplifying x + -6.102564105 = -10.022295988 Reorder the terms: -6.102564105 + x = -10.022295988 Solving -6.102564105 + x = -10.022295988 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 = -10.022295988 + 6.102564105 Combine like terms: -6.102564105 + 6.102564105 = 0.000000000 0.000000000 + x = -10.022295988 + 6.102564105 x = -10.022295988 + 6.102564105 Combine like terms: -10.022295988 + 6.102564105 = -3.919731883 x = -3.919731883 Simplifying x = -3.919731883Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.124860093, -3.919731883}
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