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Simplifying 4r2 + 6r + 12 = 0 Reorder the terms: 12 + 6r + 4r2 = 0 Solving 12 + 6r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 3r + 2r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 3r + 2r2)' equal to zero and attempt to solve: Simplifying 6 + 3r + 2r2 = 0 Solving 6 + 3r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 1.5r + r2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.5r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + 1.5r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.5r + r2 = 0 + -3 1.5r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.5r + r2 = -3 The r term is 1.5r. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5r + 0.5625 + r2 = -3 + 0.5625 Reorder the terms: 0.5625 + 1.5r + r2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + 1.5r + r2 = -2.4375 Factor a perfect square on the left side: (r + 0.75)(r + 0.75) = -2.4375 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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