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Simplifying 8r2 + 4r + -2 = 0 Reorder the terms: -2 + 4r + 8r2 = 0 Solving -2 + 4r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2r + 4r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2r + 4r2)' equal to zero and attempt to solve: Simplifying -1 + 2r + 4r2 = 0 Solving -1 + 2r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 0.5r + r2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.5r + 0.25 + r2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.5r + r2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.5r + r2 = 0 + 0.25 0.5r + r2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.5r + r2 = 0.25 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 = 0.25 + 0.0625 Reorder the terms: 0.0625 + 0.5r + r2 = 0.25 + 0.0625 Combine like terms: 0.25 + 0.0625 = 0.3125 0.0625 + 0.5r + r2 = 0.3125 Factor a perfect square on the left side: (r + 0.25)(r + 0.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (r + 0.25) equal to 0.559016994 and -0.559016994.Subproblem 1
r + 0.25 = 0.559016994 Simplifying r + 0.25 = 0.559016994 Reorder the terms: 0.25 + r = 0.559016994 Solving 0.25 + r = 0.559016994 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + r = 0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + r = 0.559016994 + -0.25 r = 0.559016994 + -0.25 Combine like terms: 0.559016994 + -0.25 = 0.309016994 r = 0.309016994 Simplifying r = 0.309016994Subproblem 2
r + 0.25 = -0.559016994 Simplifying r + 0.25 = -0.559016994 Reorder the terms: 0.25 + r = -0.559016994 Solving 0.25 + r = -0.559016994 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + r = -0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + r = -0.559016994 + -0.25 r = -0.559016994 + -0.25 Combine like terms: -0.559016994 + -0.25 = -0.809016994 r = -0.809016994 Simplifying r = -0.809016994Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.309016994, -0.809016994}Solution
r = {0.309016994, -0.809016994}
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