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Simplifying 3r2 + 6r + 24 = 0 Reorder the terms: 24 + 6r + 3r2 = 0 Solving 24 + 6r + 3r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 2r + r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + 2r + r2)' equal to zero and attempt to solve: Simplifying 8 + 2r + r2 = 0 Solving 8 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 2r + -8 + r2 = 0 + -8 Reorder the terms: 8 + -8 + 2r + r2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2r + r2 = 0 + -8 2r + r2 = 0 + -8 Combine like terms: 0 + -8 = -8 2r + r2 = -8 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 = -8 + 1 Reorder the terms: 1 + 2r + r2 = -8 + 1 Combine like terms: -8 + 1 = -7 1 + 2r + r2 = -7 Factor a perfect square on the left side: (r + 1)(r + 1) = -7 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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