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Simplifying -6m2 = 13m + 28 Reorder the terms: -6m2 = 28 + 13m Solving -6m2 = 28 + 13m Solving for variable 'm'. Reorder the terms: -28 + -13m + -6m2 = 28 + 13m + -28 + -13m Reorder the terms: -28 + -13m + -6m2 = 28 + -28 + 13m + -13m Combine like terms: 28 + -28 = 0 -28 + -13m + -6m2 = 0 + 13m + -13m -28 + -13m + -6m2 = 13m + -13m Combine like terms: 13m + -13m = 0 -28 + -13m + -6m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(28 + 13m + 6m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(28 + 13m + 6m2)' equal to zero and attempt to solve: Simplifying 28 + 13m + 6m2 = 0 Solving 28 + 13m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.666666667 + 2.166666667m + m2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + 2.166666667m + -4.666666667 + m2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + 2.166666667m + m2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + 2.166666667m + m2 = 0 + -4.666666667 2.166666667m + m2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 2.166666667m + m2 = -4.666666667 The m term is 2.166666667m. 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. 2.166666667m + 1.173611113 + m2 = -4.666666667 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667m + m2 = -4.666666667 + 1.173611113 Combine like terms: -4.666666667 + 1.173611113 = -3.493055554 1.173611113 + 2.166666667m + m2 = -3.493055554 Factor a perfect square on the left side: (m + 1.083333334)(m + 1.083333334) = -3.493055554 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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