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Simplifying (9r3 + 5r2 + 11r) + (-2r3 + 9r + -8r2) = 0 Reorder the terms: (11r + 5r2 + 9r3) + (-2r3 + 9r + -8r2) = 0 Remove parenthesis around (11r + 5r2 + 9r3) 11r + 5r2 + 9r3 + (-2r3 + 9r + -8r2) = 0 Reorder the terms: 11r + 5r2 + 9r3 + (9r + -8r2 + -2r3) = 0 Remove parenthesis around (9r + -8r2 + -2r3) 11r + 5r2 + 9r3 + 9r + -8r2 + -2r3 = 0 Reorder the terms: 11r + 9r + 5r2 + -8r2 + 9r3 + -2r3 = 0 Combine like terms: 11r + 9r = 20r 20r + 5r2 + -8r2 + 9r3 + -2r3 = 0 Combine like terms: 5r2 + -8r2 = -3r2 20r + -3r2 + 9r3 + -2r3 = 0 Combine like terms: 9r3 + -2r3 = 7r3 20r + -3r2 + 7r3 = 0 Solving 20r + -3r2 + 7r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(20 + -3r + 7r2) = 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 '(20 + -3r + 7r2)' equal to zero and attempt to solve: Simplifying 20 + -3r + 7r2 = 0 Solving 20 + -3r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.857142857 + -0.4285714286r + r2 = 0 Move the constant term to the right: Add '-2.857142857' to each side of the equation. 2.857142857 + -0.4285714286r + -2.857142857 + r2 = 0 + -2.857142857 Reorder the terms: 2.857142857 + -2.857142857 + -0.4285714286r + r2 = 0 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + -0.4285714286r + r2 = 0 + -2.857142857 -0.4285714286r + r2 = 0 + -2.857142857 Combine like terms: 0 + -2.857142857 = -2.857142857 -0.4285714286r + r2 = -2.857142857 The r term is -0.4285714286r. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286r + 0.04591836735 + r2 = -2.857142857 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286r + r2 = -2.857142857 + 0.04591836735 Combine like terms: -2.857142857 + 0.04591836735 = -2.81122448965 0.04591836735 + -0.4285714286r + r2 = -2.81122448965 Factor a perfect square on the left side: (r + -0.2142857143)(r + -0.2142857143) = -2.81122448965 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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