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Simplifying R3 + -1R2 + R = 0 Reorder the terms: R + -1R2 + R3 = 0 Solving R + -1R2 + R3 = 0 Solving for variable 'R'. Factor out the Greatest Common Factor (GCF), 'R'. R(1 + -1R + R2) = 0Subproblem 1
Set the factor 'R' equal to zero and attempt to solve: Simplifying R = 0 Solving R = 0 Move all terms containing R to the left, all other terms to the right. Simplifying R = 0Subproblem 2
Set the factor '(1 + -1R + R2)' equal to zero and attempt to solve: Simplifying 1 + -1R + R2 = 0 Solving 1 + -1R + R2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1R + -1 + R2 = 0 + -1 Reorder the terms: 1 + -1 + -1R + R2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1R + R2 = 0 + -1 -1R + R2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1R + R2 = -1 The R term is -1R. 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. -1R + 0.25 + R2 = -1 + 0.25 Reorder the terms: 0.25 + -1R + R2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1R + R2 = -0.75 Factor a perfect square on the left side: (R + -0.5)(R + -0.5) = -0.75 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.Solution
R = {0}
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