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Simplifying 6r2 + -18 = 8r Reorder the terms: -18 + 6r2 = 8r Solving -18 + 6r2 = 8r Solving for variable 'r'. Reorder the terms: -18 + -8r + 6r2 = 8r + -8r Combine like terms: 8r + -8r = 0 -18 + -8r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -4r + 3r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -4r + 3r2)' equal to zero and attempt to solve: Simplifying -9 + -4r + 3r2 = 0 Solving -9 + -4r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -1.333333333r + r2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.333333333r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + -1.333333333r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.333333333r + r2 = 0 + 3 -1.333333333r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.333333333r + r2 = 3 The r term is -1.333333333r. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333r + 0.4444444442 + r2 = 3 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333r + r2 = 3 + 0.4444444442 Combine like terms: 3 + 0.4444444442 = 3.4444444442 0.4444444442 + -1.333333333r + r2 = 3.4444444442 Factor a perfect square on the left side: (r + -0.6666666665)(r + -0.6666666665) = 3.4444444442 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (r + -0.6666666665) equal to 1.855921454 and -1.855921454.Subproblem 1
r + -0.6666666665 = 1.855921454 Simplifying r + -0.6666666665 = 1.855921454 Reorder the terms: -0.6666666665 + r = 1.855921454 Solving -0.6666666665 + r = 1.855921454 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + r = 1.855921454 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + r = 1.855921454 + 0.6666666665 r = 1.855921454 + 0.6666666665 Combine like terms: 1.855921454 + 0.6666666665 = 2.5225881205 r = 2.5225881205 Simplifying r = 2.5225881205Subproblem 2
r + -0.6666666665 = -1.855921454 Simplifying r + -0.6666666665 = -1.855921454 Reorder the terms: -0.6666666665 + r = -1.855921454 Solving -0.6666666665 + r = -1.855921454 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + r = -1.855921454 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + r = -1.855921454 + 0.6666666665 r = -1.855921454 + 0.6666666665 Combine like terms: -1.855921454 + 0.6666666665 = -1.1892547875 r = -1.1892547875 Simplifying r = -1.1892547875Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.5225881205, -1.1892547875}Solution
r = {2.5225881205, -1.1892547875}
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