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Simplifying -2r2 = r + 17 Reorder the terms: -2r2 = 17 + r Solving -2r2 = 17 + r Solving for variable 'r'. Reorder the terms: -17 + -1r + -2r2 = 17 + r + -17 + -1r Reorder the terms: -17 + -1r + -2r2 = 17 + -17 + r + -1r Combine like terms: 17 + -17 = 0 -17 + -1r + -2r2 = 0 + r + -1r -17 + -1r + -2r2 = r + -1r Combine like terms: r + -1r = 0 -17 + -1r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + r + 2r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + r + 2r2)' equal to zero and attempt to solve: Simplifying 17 + r + 2r2 = 0 Solving 17 + r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 0.5r + r2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 0.5r + -8.5 + r2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 0.5r + r2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 0.5r + r2 = 0 + -8.5 0.5r + r2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 0.5r + r2 = -8.5 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. 0.5r + 0.25 + r2 = -8.5 + 0.25 Reorder the terms: 0.25 + 0.5r + r2 = -8.5 + 0.25 Combine like terms: -8.5 + 0.25 = -8.25 0.25 + 0.5r + r2 = -8.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -8.25 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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