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Simplifying (6x + 2)(x + -3) = 9 Reorder the terms: (2 + 6x)(x + -3) = 9 Reorder the terms: (2 + 6x)(-3 + x) = 9 Multiply (2 + 6x) * (-3 + x) (2(-3 + x) + 6x * (-3 + x)) = 9 ((-3 * 2 + x * 2) + 6x * (-3 + x)) = 9 ((-6 + 2x) + 6x * (-3 + x)) = 9 (-6 + 2x + (-3 * 6x + x * 6x)) = 9 (-6 + 2x + (-18x + 6x2)) = 9 Combine like terms: 2x + -18x = -16x (-6 + -16x + 6x2) = 9 Solving -6 + -16x + 6x2 = 9 Solving for variable 'x'. Reorder the terms: -6 + -9 + -16x + 6x2 = 9 + -9 Combine like terms: -6 + -9 = -15 -15 + -16x + 6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -15 + -16x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.666666667x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.666666667x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.666666667x + x2 = 0 + 2.5 -2.666666667x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.666666667x + x2 = 2.5 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 = 2.5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.5 + 1.777777780 Combine like terms: 2.5 + 1.777777780 = 4.27777778 1.777777780 + -2.666666667x + x2 = 4.27777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.27777778 Calculate the square root of the right side: 2.068278942 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.068278942 and -2.068278942.Subproblem 1
x + -1.333333334 = 2.068278942 Simplifying x + -1.333333334 = 2.068278942 Reorder the terms: -1.333333334 + x = 2.068278942 Solving -1.333333334 + x = 2.068278942 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 = 2.068278942 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.068278942 + 1.333333334 x = 2.068278942 + 1.333333334 Combine like terms: 2.068278942 + 1.333333334 = 3.401612276 x = 3.401612276 Simplifying x = 3.401612276Subproblem 2
x + -1.333333334 = -2.068278942 Simplifying x + -1.333333334 = -2.068278942 Reorder the terms: -1.333333334 + x = -2.068278942 Solving -1.333333334 + x = -2.068278942 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 = -2.068278942 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.068278942 + 1.333333334 x = -2.068278942 + 1.333333334 Combine like terms: -2.068278942 + 1.333333334 = -0.734945608 x = -0.734945608 Simplifying x = -0.734945608Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.401612276, -0.734945608}
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