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Simplifying 5r2 + -3 = 2r + 9r2 Reorder the terms: -3 + 5r2 = 2r + 9r2 Solving -3 + 5r2 = 2r + 9r2 Solving for variable 'r'. Reorder the terms: -3 + -2r + 5r2 + -9r2 = 2r + 9r2 + -2r + -9r2 Combine like terms: 5r2 + -9r2 = -4r2 -3 + -2r + -4r2 = 2r + 9r2 + -2r + -9r2 Reorder the terms: -3 + -2r + -4r2 = 2r + -2r + 9r2 + -9r2 Combine like terms: 2r + -2r = 0 -3 + -2r + -4r2 = 0 + 9r2 + -9r2 -3 + -2r + -4r2 = 9r2 + -9r2 Combine like terms: 9r2 + -9r2 = 0 -3 + -2r + -4r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 2r + 4r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2r + 4r2)' equal to zero and attempt to solve: Simplifying 3 + 2r + 4r2 = 0 Solving 3 + 2r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.5r + r2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.5r + -0.75 + r2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.5r + r2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.5r + r2 = 0 + -0.75 0.5r + r2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.5r + r2 = -0.75 The r term is 0.5r. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5r + 0.0625 + r2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + 0.5r + r2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + 0.5r + r2 = -0.6875 Factor a perfect square on the left side: (r + 0.25)(r + 0.25) = -0.6875 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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