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Simplifying (3x + -2)(x + 4) + -1(2x + 3)(x + -6) = 0 Reorder the terms: (-2 + 3x)(x + 4) + -1(2x + 3)(x + -6) = 0 Reorder the terms: (-2 + 3x)(4 + x) + -1(2x + 3)(x + -6) = 0 Multiply (-2 + 3x) * (4 + x) (-2(4 + x) + 3x * (4 + x)) + -1(2x + 3)(x + -6) = 0 ((4 * -2 + x * -2) + 3x * (4 + x)) + -1(2x + 3)(x + -6) = 0 ((-8 + -2x) + 3x * (4 + x)) + -1(2x + 3)(x + -6) = 0 (-8 + -2x + (4 * 3x + x * 3x)) + -1(2x + 3)(x + -6) = 0 (-8 + -2x + (12x + 3x2)) + -1(2x + 3)(x + -6) = 0 Combine like terms: -2x + 12x = 10x (-8 + 10x + 3x2) + -1(2x + 3)(x + -6) = 0 Reorder the terms: -8 + 10x + 3x2 + -1(3 + 2x)(x + -6) = 0 Reorder the terms: -8 + 10x + 3x2 + -1(3 + 2x)(-6 + x) = 0 Multiply (3 + 2x) * (-6 + x) -8 + 10x + 3x2 + -1(3(-6 + x) + 2x * (-6 + x)) = 0 -8 + 10x + 3x2 + -1((-6 * 3 + x * 3) + 2x * (-6 + x)) = 0 -8 + 10x + 3x2 + -1((-18 + 3x) + 2x * (-6 + x)) = 0 -8 + 10x + 3x2 + -1(-18 + 3x + (-6 * 2x + x * 2x)) = 0 -8 + 10x + 3x2 + -1(-18 + 3x + (-12x + 2x2)) = 0 Combine like terms: 3x + -12x = -9x -8 + 10x + 3x2 + -1(-18 + -9x + 2x2) = 0 -8 + 10x + 3x2 + (-18 * -1 + -9x * -1 + 2x2 * -1) = 0 -8 + 10x + 3x2 + (18 + 9x + -2x2) = 0 Reorder the terms: -8 + 18 + 10x + 9x + 3x2 + -2x2 = 0 Combine like terms: -8 + 18 = 10 10 + 10x + 9x + 3x2 + -2x2 = 0 Combine like terms: 10x + 9x = 19x 10 + 19x + 3x2 + -2x2 = 0 Combine like terms: 3x2 + -2x2 = 1x2 10 + 19x + 1x2 = 0 Solving 10 + 19x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 19x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 19x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 19x + x2 = 0 + -10 19x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 19x + x2 = -10 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -10 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -10 + 90.25 Combine like terms: -10 + 90.25 = 80.25 90.25 + 19x + x2 = 80.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 9.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 9.5 = 8.958236434 Simplifying x + 9.5 = 8.958236434 Reorder the terms: 9.5 + x = 8.958236434 Solving 9.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 8.958236434 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.958236434 + -9.5 x = 8.958236434 + -9.5 Combine like terms: 8.958236434 + -9.5 = -0.541763566 x = -0.541763566 Simplifying x = -0.541763566Subproblem 2
x + 9.5 = -8.958236434 Simplifying x + 9.5 = -8.958236434 Reorder the terms: 9.5 + x = -8.958236434 Solving 9.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -8.958236434 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.958236434 + -9.5 x = -8.958236434 + -9.5 Combine like terms: -8.958236434 + -9.5 = -18.458236434 x = -18.458236434 Simplifying x = -18.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.541763566, -18.458236434}
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