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Simplifying 36r9 + -9r6 + 54r3 = 0 Reorder the terms: 54r3 + -9r6 + 36r9 = 0 Solving 54r3 + -9r6 + 36r9 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '9r3'. 9r3(6 + -1r3 + 4r6) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6 + -1r3 + 4r6)' equal to zero and attempt to solve: Simplifying 6 + -1r3 + 4r6 = 0 Solving 6 + -1r3 + 4r6 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -0.25r3 + r6 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.25r3 + -1.5 + r6 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.25r3 + r6 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.25r3 + r6 = 0 + -1.5 -0.25r3 + r6 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.25r3 + r6 = -1.5 The r term is -0.25r3. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25r3 + 0.015625 + r6 = -1.5 + 0.015625 Reorder the terms: 0.015625 + -0.25r3 + r6 = -1.5 + 0.015625 Combine like terms: -1.5 + 0.015625 = -1.484375 0.015625 + -0.25r3 + r6 = -1.484375 Factor a perfect square on the left side: (r3 + -0.125)(r3 + -0.125) = -1.484375 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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