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Simplifying 39x2 + -482x + -2459 = 0 Reorder the terms: -2459 + -482x + 39x2 = 0 Solving -2459 + -482x + 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 + -12.35897436x + x2 = 0 Move the constant term to the right: Add '63.05128205' to each side of the equation. -63.05128205 + -12.35897436x + 63.05128205 + x2 = 0 + 63.05128205 Reorder the terms: -63.05128205 + 63.05128205 + -12.35897436x + x2 = 0 + 63.05128205 Combine like terms: -63.05128205 + 63.05128205 = 0.00000000 0.00000000 + -12.35897436x + x2 = 0 + 63.05128205 -12.35897436x + x2 = 0 + 63.05128205 Combine like terms: 0 + 63.05128205 = 63.05128205 -12.35897436x + x2 = 63.05128205 The x term is -12.35897436x. Take half its coefficient (-6.17948718). Square it (38.18606181) and add it to both sides. Add '38.18606181' to each side of the equation. -12.35897436x + 38.18606181 + x2 = 63.05128205 + 38.18606181 Reorder the terms: 38.18606181 + -12.35897436x + x2 = 63.05128205 + 38.18606181 Combine like terms: 63.05128205 + 38.18606181 = 101.23734386 38.18606181 + -12.35897436x + x2 = 101.23734386 Factor a perfect square on the left side: (x + -6.17948718)(x + -6.17948718) = 101.23734386 Calculate the square root of the right side: 10.06167699 Break this problem into two subproblems by setting (x + -6.17948718) equal to 10.06167699 and -10.06167699.Subproblem 1
x + -6.17948718 = 10.06167699 Simplifying x + -6.17948718 = 10.06167699 Reorder the terms: -6.17948718 + x = 10.06167699 Solving -6.17948718 + x = 10.06167699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.17948718' to each side of the equation. -6.17948718 + 6.17948718 + x = 10.06167699 + 6.17948718 Combine like terms: -6.17948718 + 6.17948718 = 0.00000000 0.00000000 + x = 10.06167699 + 6.17948718 x = 10.06167699 + 6.17948718 Combine like terms: 10.06167699 + 6.17948718 = 16.24116417 x = 16.24116417 Simplifying x = 16.24116417Subproblem 2
x + -6.17948718 = -10.06167699 Simplifying x + -6.17948718 = -10.06167699 Reorder the terms: -6.17948718 + x = -10.06167699 Solving -6.17948718 + x = -10.06167699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.17948718' to each side of the equation. -6.17948718 + 6.17948718 + x = -10.06167699 + 6.17948718 Combine like terms: -6.17948718 + 6.17948718 = 0.00000000 0.00000000 + x = -10.06167699 + 6.17948718 x = -10.06167699 + 6.17948718 Combine like terms: -10.06167699 + 6.17948718 = -3.88218981 x = -3.88218981 Simplifying x = -3.88218981Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.24116417, -3.88218981}
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