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Simplifying -6x2 + -13x = 12 Reorder the terms: -13x + -6x2 = 12 Solving -13x + -6x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -13x + -6x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -13x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 13x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 13x + 6x2)' equal to zero and attempt to solve: Simplifying 12 + 13x + 6x2 = 0 Solving 12 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2.166666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2.166666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2.166666667x + x2 = 0 + -2 2.166666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2.166666667x + x2 = -2 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = -2 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = -2 + 1.173611113 Combine like terms: -2 + 1.173611113 = -0.826388887 1.173611113 + 2.166666667x + x2 = -0.826388887 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = -0.826388887 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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