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Simplifying 10r2 + 75r + 180 = 0 Reorder the terms: 180 + 75r + 10r2 = 0 Solving 180 + 75r + 10r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(36 + 15r + 2r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(36 + 15r + 2r2)' equal to zero and attempt to solve: Simplifying 36 + 15r + 2r2 = 0 Solving 36 + 15r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + 7.5r + r2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + 7.5r + -18 + r2 = 0 + -18 Reorder the terms: 18 + -18 + 7.5r + r2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 7.5r + r2 = 0 + -18 7.5r + r2 = 0 + -18 Combine like terms: 0 + -18 = -18 7.5r + r2 = -18 The r term is 7.5r. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5r + 14.0625 + r2 = -18 + 14.0625 Reorder the terms: 14.0625 + 7.5r + r2 = -18 + 14.0625 Combine like terms: -18 + 14.0625 = -3.9375 14.0625 + 7.5r + r2 = -3.9375 Factor a perfect square on the left side: (r + 3.75)(r + 3.75) = -3.9375 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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