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Simplifying -12r2 + -4r + -9 = -2 Reorder the terms: -9 + -4r + -12r2 = -2 Solving -9 + -4r + -12r2 = -2 Solving for variable 'r'. Reorder the terms: -9 + 2 + -4r + -12r2 = -2 + 2 Combine like terms: -9 + 2 = -7 -7 + -4r + -12r2 = -2 + 2 Combine like terms: -2 + 2 = 0 -7 + -4r + -12r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 4r + 12r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 4r + 12r2)' equal to zero and attempt to solve: Simplifying 7 + 4r + 12r2 = 0 Solving 7 + 4r + 12r2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 0.3333333333r + r2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 0.3333333333r + -0.5833333333 + r2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 0.3333333333r + r2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 0.3333333333r + r2 = 0 + -0.5833333333 0.3333333333r + r2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 0.3333333333r + r2 = -0.5833333333 The r term is 0.3333333333r. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333r + 0.02777777779 + r2 = -0.5833333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333r + r2 = -0.5833333333 + 0.02777777779 Combine like terms: -0.5833333333 + 0.02777777779 = -0.55555555551 0.02777777779 + 0.3333333333r + r2 = -0.55555555551 Factor a perfect square on the left side: (r + 0.1666666667)(r + 0.1666666667) = -0.55555555551 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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