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Simplifying 8r2 + -3r + -12 = 6 Reorder the terms: -12 + -3r + 8r2 = 6 Solving -12 + -3r + 8r2 = 6 Solving for variable 'r'. Reorder the terms: -12 + -6 + -3r + 8r2 = 6 + -6 Combine like terms: -12 + -6 = -18 -18 + -3r + 8r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -18 + -3r + 8r2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -0.375r + r2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.375r + 2.25 + r2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.375r + r2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.375r + r2 = 0 + 2.25 -0.375r + r2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.375r + r2 = 2.25 The r term is -0.375r. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375r + 0.03515625 + r2 = 2.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375r + r2 = 2.25 + 0.03515625 Combine like terms: 2.25 + 0.03515625 = 2.28515625 0.03515625 + -0.375r + r2 = 2.28515625 Factor a perfect square on the left side: (r + -0.1875)(r + -0.1875) = 2.28515625 Calculate the square root of the right side: 1.511673328 Break this problem into two subproblems by setting (r + -0.1875) equal to 1.511673328 and -1.511673328.Subproblem 1
r + -0.1875 = 1.511673328 Simplifying r + -0.1875 = 1.511673328 Reorder the terms: -0.1875 + r = 1.511673328 Solving -0.1875 + r = 1.511673328 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = 1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = 1.511673328 + 0.1875 r = 1.511673328 + 0.1875 Combine like terms: 1.511673328 + 0.1875 = 1.699173328 r = 1.699173328 Simplifying r = 1.699173328Subproblem 2
r + -0.1875 = -1.511673328 Simplifying r + -0.1875 = -1.511673328 Reorder the terms: -0.1875 + r = -1.511673328 Solving -0.1875 + r = -1.511673328 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = -1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = -1.511673328 + 0.1875 r = -1.511673328 + 0.1875 Combine like terms: -1.511673328 + 0.1875 = -1.324173328 r = -1.324173328 Simplifying r = -1.324173328Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.699173328, -1.324173328}
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