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