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Simplifying 4r2 + 4r + 6 = 0 Reorder the terms: 6 + 4r + 4r2 = 0 Solving 6 + 4r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2r + 2r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2r + 2r2)' equal to zero and attempt to solve: Simplifying 3 + 2r + 2r2 = 0 Solving 3 + 2r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + r + r2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + r + -1.5 + r2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + r + r2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r + r2 = 0 + -1.5 r + r2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 r + r2 = -1.5 The r term is r. 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. + 0.25 + r2 = -1.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 1.25 + r2 = -1.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -1.25 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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