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Simplifying 11x + -6 = 4x(3x + 4) Reorder the terms: -6 + 11x = 4x(3x + 4) Reorder the terms: -6 + 11x = 4x(4 + 3x) -6 + 11x = (4 * 4x + 3x * 4x) -6 + 11x = (16x + 12x2) Solving -6 + 11x = 16x + 12x2 Solving for variable 'x'. Combine like terms: 11x + -16x = -5x -6 + -5x + -12x2 = 16x + 12x2 + -16x + -12x2 Reorder the terms: -6 + -5x + -12x2 = 16x + -16x + 12x2 + -12x2 Combine like terms: 16x + -16x = 0 -6 + -5x + -12x2 = 0 + 12x2 + -12x2 -6 + -5x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -6 + -5x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 5x + 12x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 12x2 = 0 Solving 6 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.4166666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.4166666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.4166666667x + x2 = 0 + -0.5 0.4166666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.4166666667x + x2 = -0.5 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = -0.5 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = -0.5 + 0.04340277781 Combine like terms: -0.5 + 0.04340277781 = -0.45659722219 0.04340277781 + 0.4166666667x + x2 = -0.45659722219 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = -0.45659722219 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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