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Simplifying -12c2 + 26c = 56 Reorder the terms: 26c + -12c2 = 56 Solving 26c + -12c2 = 56 Solving for variable 'c'. Reorder the terms: -56 + 26c + -12c2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 26c + -12c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 13c + -6c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + 13c + -6c2)' equal to zero and attempt to solve: Simplifying -28 + 13c + -6c2 = 0 Solving -28 + 13c + -6c2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 4.666666667 + -2.166666667c + c2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -2.166666667c + -4.666666667 + c2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -2.166666667c + c2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -2.166666667c + c2 = 0 + -4.666666667 -2.166666667c + c2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -2.166666667c + c2 = -4.666666667 The c term is -2.166666667c. 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. -2.166666667c + 1.173611113 + c2 = -4.666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667c + c2 = -4.666666667 + 1.173611113 Combine like terms: -4.666666667 + 1.173611113 = -3.493055554 1.173611113 + -2.166666667c + c2 = -3.493055554 Factor a perfect square on the left side: (c + -1.083333334)(c + -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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