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Simplifying 8r2 + -40r + -122 = 0 Reorder the terms: -122 + -40r + 8r2 = 0 Solving -122 + -40r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + -20r + 4r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + -20r + 4r2)' equal to zero and attempt to solve: Simplifying -61 + -20r + 4r2 = 0 Solving -61 + -20r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15.25 + -5r + r2 = 0 Move the constant term to the right: Add '15.25' to each side of the equation. -15.25 + -5r + 15.25 + r2 = 0 + 15.25 Reorder the terms: -15.25 + 15.25 + -5r + r2 = 0 + 15.25 Combine like terms: -15.25 + 15.25 = 0.00 0.00 + -5r + r2 = 0 + 15.25 -5r + r2 = 0 + 15.25 Combine like terms: 0 + 15.25 = 15.25 -5r + r2 = 15.25 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = 15.25 + 6.25 Reorder the terms: 6.25 + -5r + r2 = 15.25 + 6.25 Combine like terms: 15.25 + 6.25 = 21.5 6.25 + -5r + r2 = 21.5 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (r + -2.5) equal to 4.636809248 and -4.636809248.Subproblem 1
r + -2.5 = 4.636809248 Simplifying r + -2.5 = 4.636809248 Reorder the terms: -2.5 + r = 4.636809248 Solving -2.5 + r = 4.636809248 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = 4.636809248 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 4.636809248 + 2.5 r = 4.636809248 + 2.5 Combine like terms: 4.636809248 + 2.5 = 7.136809248 r = 7.136809248 Simplifying r = 7.136809248Subproblem 2
r + -2.5 = -4.636809248 Simplifying r + -2.5 = -4.636809248 Reorder the terms: -2.5 + r = -4.636809248 Solving -2.5 + r = -4.636809248 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = -4.636809248 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -4.636809248 + 2.5 r = -4.636809248 + 2.5 Combine like terms: -4.636809248 + 2.5 = -2.136809248 r = -2.136809248 Simplifying r = -2.136809248Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.136809248, -2.136809248}Solution
r = {7.136809248, -2.136809248}
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