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Simplifying 6x2 + -247x + 360 = 0 Reorder the terms: 360 + -247x + 6x2 = 0 Solving 360 + -247x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 60 + -41.16666667x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -41.16666667x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -41.16666667x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -41.16666667x + x2 = 0 + -60 -41.16666667x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -41.16666667x + x2 = -60 The x term is -41.16666667x. Take half its coefficient (-20.58333334). Square it (423.6736114) and add it to both sides. Add '423.6736114' to each side of the equation. -41.16666667x + 423.6736114 + x2 = -60 + 423.6736114 Reorder the terms: 423.6736114 + -41.16666667x + x2 = -60 + 423.6736114 Combine like terms: -60 + 423.6736114 = 363.6736114 423.6736114 + -41.16666667x + x2 = 363.6736114 Factor a perfect square on the left side: (x + -20.58333334)(x + -20.58333334) = 363.6736114 Calculate the square root of the right side: 19.070228405 Break this problem into two subproblems by setting (x + -20.58333334) equal to 19.070228405 and -19.070228405.Subproblem 1
x + -20.58333334 = 19.070228405 Simplifying x + -20.58333334 = 19.070228405 Reorder the terms: -20.58333334 + x = 19.070228405 Solving -20.58333334 + x = 19.070228405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.58333334' to each side of the equation. -20.58333334 + 20.58333334 + x = 19.070228405 + 20.58333334 Combine like terms: -20.58333334 + 20.58333334 = 0.00000000 0.00000000 + x = 19.070228405 + 20.58333334 x = 19.070228405 + 20.58333334 Combine like terms: 19.070228405 + 20.58333334 = 39.653561745 x = 39.653561745 Simplifying x = 39.653561745Subproblem 2
x + -20.58333334 = -19.070228405 Simplifying x + -20.58333334 = -19.070228405 Reorder the terms: -20.58333334 + x = -19.070228405 Solving -20.58333334 + x = -19.070228405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.58333334' to each side of the equation. -20.58333334 + 20.58333334 + x = -19.070228405 + 20.58333334 Combine like terms: -20.58333334 + 20.58333334 = 0.00000000 0.00000000 + x = -19.070228405 + 20.58333334 x = -19.070228405 + 20.58333334 Combine like terms: -19.070228405 + 20.58333334 = 1.513104935 x = 1.513104935 Simplifying x = 1.513104935Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.653561745, 1.513104935}
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