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Simplifying 8r2 + 8r + -3 = -11 Reorder the terms: -3 + 8r + 8r2 = -11 Solving -3 + 8r + 8r2 = -11 Solving for variable 'r'. Reorder the terms: -3 + 11 + 8r + 8r2 = -11 + 11 Combine like terms: -3 + 11 = 8 8 + 8r + 8r2 = -11 + 11 Combine like terms: -11 + 11 = 0 8 + 8r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + r + r2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + r + r2)' equal to zero and attempt to solve: Simplifying 1 + r + r2 = 0 Solving 1 + r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r + r2 = 0 + -1 r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 r + r2 = -1 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. r + 0.25 + r2 = -1 + 0.25 Reorder the terms: 0.25 + r + r2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + r + r2 = -0.75 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -0.75 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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