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Simplifying (2x + 3)(x + -6) + -1(5x + 3)(3x + 4) = 0 Reorder the terms: (3 + 2x)(x + -6) + -1(5x + 3)(3x + 4) = 0 Reorder the terms: (3 + 2x)(-6 + x) + -1(5x + 3)(3x + 4) = 0 Multiply (3 + 2x) * (-6 + x) (3(-6 + x) + 2x * (-6 + x)) + -1(5x + 3)(3x + 4) = 0 ((-6 * 3 + x * 3) + 2x * (-6 + x)) + -1(5x + 3)(3x + 4) = 0 ((-18 + 3x) + 2x * (-6 + x)) + -1(5x + 3)(3x + 4) = 0 (-18 + 3x + (-6 * 2x + x * 2x)) + -1(5x + 3)(3x + 4) = 0 (-18 + 3x + (-12x + 2x2)) + -1(5x + 3)(3x + 4) = 0 Combine like terms: 3x + -12x = -9x (-18 + -9x + 2x2) + -1(5x + 3)(3x + 4) = 0 Reorder the terms: -18 + -9x + 2x2 + -1(3 + 5x)(3x + 4) = 0 Reorder the terms: -18 + -9x + 2x2 + -1(3 + 5x)(4 + 3x) = 0 Multiply (3 + 5x) * (4 + 3x) -18 + -9x + 2x2 + -1(3(4 + 3x) + 5x * (4 + 3x)) = 0 -18 + -9x + 2x2 + -1((4 * 3 + 3x * 3) + 5x * (4 + 3x)) = 0 -18 + -9x + 2x2 + -1((12 + 9x) + 5x * (4 + 3x)) = 0 -18 + -9x + 2x2 + -1(12 + 9x + (4 * 5x + 3x * 5x)) = 0 -18 + -9x + 2x2 + -1(12 + 9x + (20x + 15x2)) = 0 Combine like terms: 9x + 20x = 29x -18 + -9x + 2x2 + -1(12 + 29x + 15x2) = 0 -18 + -9x + 2x2 + (12 * -1 + 29x * -1 + 15x2 * -1) = 0 -18 + -9x + 2x2 + (-12 + -29x + -15x2) = 0 Reorder the terms: -18 + -12 + -9x + -29x + 2x2 + -15x2 = 0 Combine like terms: -18 + -12 = -30 -30 + -9x + -29x + 2x2 + -15x2 = 0 Combine like terms: -9x + -29x = -38x -30 + -38x + 2x2 + -15x2 = 0 Combine like terms: 2x2 + -15x2 = -13x2 -30 + -38x + -13x2 = 0 Solving -30 + -38x + -13x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + 38x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(30 + 38x + 13x2)' equal to zero and attempt to solve: Simplifying 30 + 38x + 13x2 = 0 Solving 30 + 38x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 2.307692308 + 2.923076923x + x2 = 0 Move the constant term to the right: Add '-2.307692308' to each side of the equation. 2.307692308 + 2.923076923x + -2.307692308 + x2 = 0 + -2.307692308 Reorder the terms: 2.307692308 + -2.307692308 + 2.923076923x + x2 = 0 + -2.307692308 Combine like terms: 2.307692308 + -2.307692308 = 0.000000000 0.000000000 + 2.923076923x + x2 = 0 + -2.307692308 2.923076923x + x2 = 0 + -2.307692308 Combine like terms: 0 + -2.307692308 = -2.307692308 2.923076923x + x2 = -2.307692308 The x term is 2.923076923x. Take half its coefficient (1.461538462). Square it (2.136094676) and add it to both sides. Add '2.136094676' to each side of the equation. 2.923076923x + 2.136094676 + x2 = -2.307692308 + 2.136094676 Reorder the terms: 2.136094676 + 2.923076923x + x2 = -2.307692308 + 2.136094676 Combine like terms: -2.307692308 + 2.136094676 = -0.171597632 2.136094676 + 2.923076923x + x2 = -0.171597632 Factor a perfect square on the left side: (x + 1.461538462)(x + 1.461538462) = -0.171597632 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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