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Simplifying (6x + -4)(x + 2) = 2(11x + -19) + 2(3x + -13) Reorder the terms: (-4 + 6x)(x + 2) = 2(11x + -19) + 2(3x + -13) Reorder the terms: (-4 + 6x)(2 + x) = 2(11x + -19) + 2(3x + -13) Multiply (-4 + 6x) * (2 + x) (-4(2 + x) + 6x * (2 + x)) = 2(11x + -19) + 2(3x + -13) ((2 * -4 + x * -4) + 6x * (2 + x)) = 2(11x + -19) + 2(3x + -13) ((-8 + -4x) + 6x * (2 + x)) = 2(11x + -19) + 2(3x + -13) (-8 + -4x + (2 * 6x + x * 6x)) = 2(11x + -19) + 2(3x + -13) (-8 + -4x + (12x + 6x2)) = 2(11x + -19) + 2(3x + -13) Combine like terms: -4x + 12x = 8x (-8 + 8x + 6x2) = 2(11x + -19) + 2(3x + -13) Reorder the terms: -8 + 8x + 6x2 = 2(-19 + 11x) + 2(3x + -13) -8 + 8x + 6x2 = (-19 * 2 + 11x * 2) + 2(3x + -13) -8 + 8x + 6x2 = (-38 + 22x) + 2(3x + -13) Reorder the terms: -8 + 8x + 6x2 = -38 + 22x + 2(-13 + 3x) -8 + 8x + 6x2 = -38 + 22x + (-13 * 2 + 3x * 2) -8 + 8x + 6x2 = -38 + 22x + (-26 + 6x) Reorder the terms: -8 + 8x + 6x2 = -38 + -26 + 22x + 6x Combine like terms: -38 + -26 = -64 -8 + 8x + 6x2 = -64 + 22x + 6x Combine like terms: 22x + 6x = 28x -8 + 8x + 6x2 = -64 + 28x Solving -8 + 8x + 6x2 = -64 + 28x Solving for variable 'x'. Reorder the terms: -8 + 64 + 8x + -28x + 6x2 = -64 + 28x + 64 + -28x Combine like terms: -8 + 64 = 56 56 + 8x + -28x + 6x2 = -64 + 28x + 64 + -28x Combine like terms: 8x + -28x = -20x 56 + -20x + 6x2 = -64 + 28x + 64 + -28x Reorder the terms: 56 + -20x + 6x2 = -64 + 64 + 28x + -28x Combine like terms: -64 + 64 = 0 56 + -20x + 6x2 = 0 + 28x + -28x 56 + -20x + 6x2 = 28x + -28x Combine like terms: 28x + -28x = 0 56 + -20x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -10x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + -10x + 3x2)' equal to zero and attempt to solve: Simplifying 28 + -10x + 3x2 = 0 Solving 28 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -3.333333333x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -3.333333333x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + -9.333333333 -3.333333333x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -3.333333333x + x2 = -9.333333333 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -9.333333333 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -9.333333333 + 2.777777779 Combine like terms: -9.333333333 + 2.777777779 = -6.555555554 2.777777779 + -3.333333333x + x2 = -6.555555554 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = -6.555555554 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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