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Simplifying 8x + -5(2x + 3) + -1(1 + -6x) = 8x(4 + 6x) Reorder the terms: 8x + -5(3 + 2x) + -1(1 + -6x) = 8x(4 + 6x) 8x + (3 * -5 + 2x * -5) + -1(1 + -6x) = 8x(4 + 6x) 8x + (-15 + -10x) + -1(1 + -6x) = 8x(4 + 6x) 8x + -15 + -10x + (1 * -1 + -6x * -1) = 8x(4 + 6x) 8x + -15 + -10x + (-1 + 6x) = 8x(4 + 6x) Reorder the terms: -15 + -1 + 8x + -10x + 6x = 8x(4 + 6x) Combine like terms: -15 + -1 = -16 -16 + 8x + -10x + 6x = 8x(4 + 6x) Combine like terms: 8x + -10x = -2x -16 + -2x + 6x = 8x(4 + 6x) Combine like terms: -2x + 6x = 4x -16 + 4x = 8x(4 + 6x) -16 + 4x = (4 * 8x + 6x * 8x) -16 + 4x = (32x + 48x2) Solving -16 + 4x = 32x + 48x2 Solving for variable 'x'. Combine like terms: 4x + -32x = -28x -16 + -28x + -48x2 = 32x + 48x2 + -32x + -48x2 Reorder the terms: -16 + -28x + -48x2 = 32x + -32x + 48x2 + -48x2 Combine like terms: 32x + -32x = 0 -16 + -28x + -48x2 = 0 + 48x2 + -48x2 -16 + -28x + -48x2 = 48x2 + -48x2 Combine like terms: 48x2 + -48x2 = 0 -16 + -28x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(4 + 7x + 12x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(4 + 7x + 12x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + 12x2 = 0 Solving 4 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.5833333333x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.5833333333x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.5833333333x + x2 = 0 + -0.3333333333 0.5833333333x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.5833333333x + x2 = -0.3333333333 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = -0.3333333333 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = -0.3333333333 + 0.08506944446 Combine like terms: -0.3333333333 + 0.08506944446 = -0.24826388884 0.08506944446 + 0.5833333333x + x2 = -0.24826388884 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = -0.24826388884 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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