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Simplifying 9r2 = 3r + -30 Reorder the terms: 9r2 = -30 + 3r Solving 9r2 = -30 + 3r Solving for variable 'r'. Reorder the terms: 30 + -3r + 9r2 = -30 + 3r + 30 + -3r Reorder the terms: 30 + -3r + 9r2 = -30 + 30 + 3r + -3r Combine like terms: -30 + 30 = 0 30 + -3r + 9r2 = 0 + 3r + -3r 30 + -3r + 9r2 = 3r + -3r Combine like terms: 3r + -3r = 0 30 + -3r + 9r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -1r + 3r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -1r + 3r2)' equal to zero and attempt to solve: Simplifying 10 + -1r + 3r2 = 0 Solving 10 + -1r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -0.3333333333r + r2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -0.3333333333r + -3.333333333 + r2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -0.3333333333r + r2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -0.3333333333r + r2 = 0 + -3.333333333 -0.3333333333r + r2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -0.3333333333r + r2 = -3.333333333 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 = -3.333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333r + r2 = -3.333333333 + 0.02777777779 Combine like terms: -3.333333333 + 0.02777777779 = -3.30555555521 0.02777777779 + -0.3333333333r + r2 = -3.30555555521 Factor a perfect square on the left side: (r + -0.1666666667)(r + -0.1666666667) = -3.30555555521 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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