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Simplifying 6x2 + 6x + -18 = 35x + 38 Reorder the terms: -18 + 6x + 6x2 = 35x + 38 Reorder the terms: -18 + 6x + 6x2 = 38 + 35x Solving -18 + 6x + 6x2 = 38 + 35x Solving for variable 'x'. Reorder the terms: -18 + -38 + 6x + -35x + 6x2 = 38 + 35x + -38 + -35x Combine like terms: -18 + -38 = -56 -56 + 6x + -35x + 6x2 = 38 + 35x + -38 + -35x Combine like terms: 6x + -35x = -29x -56 + -29x + 6x2 = 38 + 35x + -38 + -35x Reorder the terms: -56 + -29x + 6x2 = 38 + -38 + 35x + -35x Combine like terms: 38 + -38 = 0 -56 + -29x + 6x2 = 0 + 35x + -35x -56 + -29x + 6x2 = 35x + -35x Combine like terms: 35x + -35x = 0 -56 + -29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -9.333333333 + -4.833333333x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -4.833333333x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -4.833333333x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -4.833333333x + x2 = 0 + 9.333333333 -4.833333333x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -4.833333333x + x2 = 9.333333333 The x term is -4.833333333x. Take half its coefficient (-2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. -4.833333333x + 5.840277779 + x2 = 9.333333333 + 5.840277779 Reorder the terms: 5.840277779 + -4.833333333x + x2 = 9.333333333 + 5.840277779 Combine like terms: 9.333333333 + 5.840277779 = 15.173611112 5.840277779 + -4.833333333x + x2 = 15.173611112 Factor a perfect square on the left side: (x + -2.416666667)(x + -2.416666667) = 15.173611112 Calculate the square root of the right side: 3.895331964 Break this problem into two subproblems by setting (x + -2.416666667) equal to 3.895331964 and -3.895331964.Subproblem 1
x + -2.416666667 = 3.895331964 Simplifying x + -2.416666667 = 3.895331964 Reorder the terms: -2.416666667 + x = 3.895331964 Solving -2.416666667 + x = 3.895331964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = 3.895331964 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = 3.895331964 + 2.416666667 x = 3.895331964 + 2.416666667 Combine like terms: 3.895331964 + 2.416666667 = 6.311998631 x = 6.311998631 Simplifying x = 6.311998631Subproblem 2
x + -2.416666667 = -3.895331964 Simplifying x + -2.416666667 = -3.895331964 Reorder the terms: -2.416666667 + x = -3.895331964 Solving -2.416666667 + x = -3.895331964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = -3.895331964 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = -3.895331964 + 2.416666667 x = -3.895331964 + 2.416666667 Combine like terms: -3.895331964 + 2.416666667 = -1.478665297 x = -1.478665297 Simplifying x = -1.478665297Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.311998631, -1.478665297}
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