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Simplifying 6r2 + -3r = -12 Reorder the terms: -3r + 6r2 = -12 Solving -3r + 6r2 = -12 Solving for variable 'r'. Reorder the terms: 12 + -3r + 6r2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -3r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -1r + 2r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -1r + 2r2)' equal to zero and attempt to solve: Simplifying 4 + -1r + 2r2 = 0 Solving 4 + -1r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -0.5r + r2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5r + r2 = 0 + -2 -0.5r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5r + r2 = -2 The r term is -0.5r. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5r + 0.0625 + r2 = -2 + 0.0625 Reorder the terms: 0.0625 + -0.5r + r2 = -2 + 0.0625 Combine like terms: -2 + 0.0625 = -1.9375 0.0625 + -0.5r + r2 = -1.9375 Factor a perfect square on the left side: (r + -0.25)(r + -0.25) = -1.9375 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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