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Simplifying 9r2 + 3 = 9r Reorder the terms: 3 + 9r2 = 9r Solving 3 + 9r2 = 9r Solving for variable 'r'. Reorder the terms: 3 + -9r + 9r2 = 9r + -9r Combine like terms: 9r + -9r = 0 3 + -9r + 9r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -3r + 3r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3r + 3r2)' equal to zero and attempt to solve: Simplifying 1 + -3r + 3r2 = 0 Solving 1 + -3r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -1r + r2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1r + -0.3333333333 + r2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1r + r2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1r + r2 = 0 + -0.3333333333 -1r + r2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1r + r2 = -0.3333333333 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + -1r + r2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + -1r + r2 = -0.0833333333 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = -0.0833333333 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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