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Simplifying 12r2 + 4r = -10 Reorder the terms: 4r + 12r2 = -10 Solving 4r + 12r2 = -10 Solving for variable 'r'. Reorder the terms: 10 + 4r + 12r2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 4r + 12r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 2r + 6r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2r + 6r2)' equal to zero and attempt to solve: Simplifying 5 + 2r + 6r2 = 0 Solving 5 + 2r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.3333333333r + r2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.3333333333r + -0.8333333333 + r2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.3333333333r + r2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.3333333333r + r2 = 0 + -0.8333333333 0.3333333333r + r2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.3333333333r + r2 = -0.8333333333 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 = -0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333r + r2 = -0.8333333333 + 0.02777777779 Combine like terms: -0.8333333333 + 0.02777777779 = -0.80555555551 0.02777777779 + 0.3333333333r + r2 = -0.80555555551 Factor a perfect square on the left side: (r + 0.1666666667)(r + 0.1666666667) = -0.80555555551 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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