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Simplifying 2r2 + 6r + 72 = 0 Reorder the terms: 72 + 6r + 2r2 = 0 Solving 72 + 6r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 3r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 3r + r2)' equal to zero and attempt to solve: Simplifying 36 + 3r + r2 = 0 Solving 36 + 3r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 3r + -36 + r2 = 0 + -36 Reorder the terms: 36 + -36 + 3r + r2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 3r + r2 = 0 + -36 3r + r2 = 0 + -36 Combine like terms: 0 + -36 = -36 3r + r2 = -36 The r term is 3r. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3r + 2.25 + r2 = -36 + 2.25 Reorder the terms: 2.25 + 3r + r2 = -36 + 2.25 Combine like terms: -36 + 2.25 = -33.75 2.25 + 3r + r2 = -33.75 Factor a perfect square on the left side: (r + 1.5)(r + 1.5) = -33.75 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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