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Simplifying (3x + -2)(x + 6) = -9 Reorder the terms: (-2 + 3x)(x + 6) = -9 Reorder the terms: (-2 + 3x)(6 + x) = -9 Multiply (-2 + 3x) * (6 + x) (-2(6 + x) + 3x * (6 + x)) = -9 ((6 * -2 + x * -2) + 3x * (6 + x)) = -9 ((-12 + -2x) + 3x * (6 + x)) = -9 (-12 + -2x + (6 * 3x + x * 3x)) = -9 (-12 + -2x + (18x + 3x2)) = -9 Combine like terms: -2x + 18x = 16x (-12 + 16x + 3x2) = -9 Solving -12 + 16x + 3x2 = -9 Solving for variable 'x'. Reorder the terms: -12 + 9 + 16x + 3x2 = -9 + 9 Combine like terms: -12 + 9 = -3 -3 + 16x + 3x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -3 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 5.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 5.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5.333333333x + x2 = 0 + 1 5.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 5.333333333x + x2 = 1 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 1 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 1 + 7.111111113 Combine like terms: 1 + 7.111111113 = 8.111111113 7.111111113 + 5.333333333x + x2 = 8.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 8.111111113 Calculate the square root of the right side: 2.848001249 Break this problem into two subproblems by setting (x + 2.666666667) equal to 2.848001249 and -2.848001249.Subproblem 1
x + 2.666666667 = 2.848001249 Simplifying x + 2.666666667 = 2.848001249 Reorder the terms: 2.666666667 + x = 2.848001249 Solving 2.666666667 + x = 2.848001249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 2.848001249 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 2.848001249 + -2.666666667 x = 2.848001249 + -2.666666667 Combine like terms: 2.848001249 + -2.666666667 = 0.181334582 x = 0.181334582 Simplifying x = 0.181334582Subproblem 2
x + 2.666666667 = -2.848001249 Simplifying x + 2.666666667 = -2.848001249 Reorder the terms: 2.666666667 + x = -2.848001249 Solving 2.666666667 + x = -2.848001249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -2.848001249 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -2.848001249 + -2.666666667 x = -2.848001249 + -2.666666667 Combine like terms: -2.848001249 + -2.666666667 = -5.514667916 x = -5.514667916 Simplifying x = -5.514667916Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181334582, -5.514667916}
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