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Simplifying -6r2 + -7r + -17 = -8 Reorder the terms: -17 + -7r + -6r2 = -8 Solving -17 + -7r + -6r2 = -8 Solving for variable 'r'. Reorder the terms: -17 + 8 + -7r + -6r2 = -8 + 8 Combine like terms: -17 + 8 = -9 -9 + -7r + -6r2 = -8 + 8 Combine like terms: -8 + 8 = 0 -9 + -7r + -6r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 7r + 6r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 7r + 6r2)' equal to zero and attempt to solve: Simplifying 9 + 7r + 6r2 = 0 Solving 9 + 7r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + 1.166666667r + r2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.166666667r + -1.5 + r2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.166666667r + r2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.166666667r + r2 = 0 + -1.5 1.166666667r + r2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.166666667r + r2 = -1.5 The r term is 1.166666667r. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667r + 0.3402777780 + r2 = -1.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667r + r2 = -1.5 + 0.3402777780 Combine like terms: -1.5 + 0.3402777780 = -1.159722222 0.3402777780 + 1.166666667r + r2 = -1.159722222 Factor a perfect square on the left side: (r + 0.5833333335)(r + 0.5833333335) = -1.159722222 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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