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Simplifying 18(r2 + 8r + 63) = 0 Reorder the terms: 18(63 + 8r + r2) = 0 (63 * 18 + 8r * 18 + r2 * 18) = 0 (1134 + 144r + 18r2) = 0 Solving 1134 + 144r + 18r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '18'. 18(63 + 8r + r2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(63 + 8r + r2)' equal to zero and attempt to solve: Simplifying 63 + 8r + r2 = 0 Solving 63 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 8r + -63 + r2 = 0 + -63 Reorder the terms: 63 + -63 + 8r + r2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 8r + r2 = 0 + -63 8r + r2 = 0 + -63 Combine like terms: 0 + -63 = -63 8r + r2 = -63 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = -63 + 16 Reorder the terms: 16 + 8r + r2 = -63 + 16 Combine like terms: -63 + 16 = -47 16 + 8r + r2 = -47 Factor a perfect square on the left side: (r + 4)(r + 4) = -47 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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