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Simplifying 3x2 + -8x + -180 = 0 Reorder the terms: -180 + -8x + 3x2 = 0 Solving -180 + -8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -2.666666667x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -2.666666667x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -2.666666667x + x2 = 0 + 60 -2.666666667x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -2.666666667x + x2 = 60 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 60 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 60 + 1.777777780 Combine like terms: 60 + 1.777777780 = 61.77777778 1.777777780 + -2.666666667x + x2 = 61.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 61.77777778 Calculate the square root of the right side: 7.859884082 Break this problem into two subproblems by setting (x + -1.333333334) equal to 7.859884082 and -7.859884082.Subproblem 1
x + -1.333333334 = 7.859884082 Simplifying x + -1.333333334 = 7.859884082 Reorder the terms: -1.333333334 + x = 7.859884082 Solving -1.333333334 + x = 7.859884082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 7.859884082 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 7.859884082 + 1.333333334 x = 7.859884082 + 1.333333334 Combine like terms: 7.859884082 + 1.333333334 = 9.193217416 x = 9.193217416 Simplifying x = 9.193217416Subproblem 2
x + -1.333333334 = -7.859884082 Simplifying x + -1.333333334 = -7.859884082 Reorder the terms: -1.333333334 + x = -7.859884082 Solving -1.333333334 + x = -7.859884082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -7.859884082 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -7.859884082 + 1.333333334 x = -7.859884082 + 1.333333334 Combine like terms: -7.859884082 + 1.333333334 = -6.526550748 x = -6.526550748 Simplifying x = -6.526550748Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.193217416, -6.526550748}
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