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Simplifying 4(4x + 7) + 4(x + -11) = 6x(x + 2) Reorder the terms: 4(7 + 4x) + 4(x + -11) = 6x(x + 2) (7 * 4 + 4x * 4) + 4(x + -11) = 6x(x + 2) (28 + 16x) + 4(x + -11) = 6x(x + 2) Reorder the terms: 28 + 16x + 4(-11 + x) = 6x(x + 2) 28 + 16x + (-11 * 4 + x * 4) = 6x(x + 2) 28 + 16x + (-44 + 4x) = 6x(x + 2) Reorder the terms: 28 + -44 + 16x + 4x = 6x(x + 2) Combine like terms: 28 + -44 = -16 -16 + 16x + 4x = 6x(x + 2) Combine like terms: 16x + 4x = 20x -16 + 20x = 6x(x + 2) Reorder the terms: -16 + 20x = 6x(2 + x) -16 + 20x = (2 * 6x + x * 6x) -16 + 20x = (12x + 6x2) Solving -16 + 20x = 12x + 6x2 Solving for variable 'x'. Combine like terms: 20x + -12x = 8x -16 + 8x + -6x2 = 12x + 6x2 + -12x + -6x2 Reorder the terms: -16 + 8x + -6x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 -16 + 8x + -6x2 = 0 + 6x2 + -6x2 -16 + 8x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -16 + 8x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 4x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -8 + 4x + -3x2 = 0 Solving -8 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.666666667 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -1.333333333x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -1.333333333x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -2.666666667 -1.333333333x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -1.333333333x + x2 = -2.666666667 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -2.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -2.666666667 + 0.4444444442 Combine like terms: -2.666666667 + 0.4444444442 = -2.2222222228 0.4444444442 + -1.333333333x + x2 = -2.2222222228 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -2.2222222228 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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