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Simplifying 8r2 + 6r + -18 = 6 Reorder the terms: -18 + 6r + 8r2 = 6 Solving -18 + 6r + 8r2 = 6 Solving for variable 'r'. Reorder the terms: -18 + -6 + 6r + 8r2 = 6 + -6 Combine like terms: -18 + -6 = -24 -24 + 6r + 8r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -24 + 6r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 3r + 4r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 3r + 4r2)' equal to zero and attempt to solve: Simplifying -12 + 3r + 4r2 = 0 Solving -12 + 3r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 0.75r + r2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.75r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + 0.75r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.75r + r2 = 0 + 3 0.75r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.75r + r2 = 3 The r term is 0.75r. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75r + 0.140625 + r2 = 3 + 0.140625 Reorder the terms: 0.140625 + 0.75r + r2 = 3 + 0.140625 Combine like terms: 3 + 0.140625 = 3.140625 0.140625 + 0.75r + r2 = 3.140625 Factor a perfect square on the left side: (r + 0.375)(r + 0.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (r + 0.375) equal to 1.77218086 and -1.77218086.Subproblem 1
r + 0.375 = 1.77218086 Simplifying r + 0.375 = 1.77218086 Reorder the terms: 0.375 + r = 1.77218086 Solving 0.375 + r = 1.77218086 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + r = 1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + r = 1.77218086 + -0.375 r = 1.77218086 + -0.375 Combine like terms: 1.77218086 + -0.375 = 1.39718086 r = 1.39718086 Simplifying r = 1.39718086Subproblem 2
r + 0.375 = -1.77218086 Simplifying r + 0.375 = -1.77218086 Reorder the terms: 0.375 + r = -1.77218086 Solving 0.375 + r = -1.77218086 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + r = -1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + r = -1.77218086 + -0.375 r = -1.77218086 + -0.375 Combine like terms: -1.77218086 + -0.375 = -2.14718086 r = -2.14718086 Simplifying r = -2.14718086Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.39718086, -2.14718086}Solution
r = {1.39718086, -2.14718086}
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