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Simplifying 27r * 27r + 267r + 216 = 0 Reorder the terms for easier multiplication: 27 * 27r * r + 267r + 216 = 0 Multiply 27 * 27 729r * r + 267r + 216 = 0 Multiply r * r 729r2 + 267r + 216 = 0 Reorder the terms: 216 + 267r + 729r2 = 0 Solving 216 + 267r + 729r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(72 + 89r + 243r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(72 + 89r + 243r2)' equal to zero and attempt to solve: Simplifying 72 + 89r + 243r2 = 0 Solving 72 + 89r + 243r2 = 0 Begin completing the square. Divide all terms by 243 the coefficient of the squared term: Divide each side by '243'. 0.2962962963 + 0.366255144r + r2 = 0 Move the constant term to the right: Add '-0.2962962963' to each side of the equation. 0.2962962963 + 0.366255144r + -0.2962962963 + r2 = 0 + -0.2962962963 Reorder the terms: 0.2962962963 + -0.2962962963 + 0.366255144r + r2 = 0 + -0.2962962963 Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000 0.0000000000 + 0.366255144r + r2 = 0 + -0.2962962963 0.366255144r + r2 = 0 + -0.2962962963 Combine like terms: 0 + -0.2962962963 = -0.2962962963 0.366255144r + r2 = -0.2962962963 The r term is 0.366255144r. Take half its coefficient (0.183127572). Square it (0.03353570763) and add it to both sides. Add '0.03353570763' to each side of the equation. 0.366255144r + 0.03353570763 + r2 = -0.2962962963 + 0.03353570763 Reorder the terms: 0.03353570763 + 0.366255144r + r2 = -0.2962962963 + 0.03353570763 Combine like terms: -0.2962962963 + 0.03353570763 = -0.26276058867 0.03353570763 + 0.366255144r + r2 = -0.26276058867 Factor a perfect square on the left side: (r + 0.183127572)(r + 0.183127572) = -0.26276058867 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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