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Simplifying 9 + -1(8r2 + 2r) = 0 Reorder the terms: 9 + -1(2r + 8r2) = 0 9 + (2r * -1 + 8r2 * -1) = 0 9 + (-2r + -8r2) = 0 Solving 9 + -2r + -8r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + 0.25r + r2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.25r + 1.125 + r2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.25r + r2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.25r + r2 = 0 + 1.125 0.25r + r2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.25r + r2 = 1.125 The r term is 0.25r. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25r + 0.015625 + r2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + 0.25r + r2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + 0.25r + r2 = 1.140625 Factor a perfect square on the left side: (r + 0.125)(r + 0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (r + 0.125) equal to 1.068000468 and -1.068000468.Subproblem 1
r + 0.125 = 1.068000468 Simplifying r + 0.125 = 1.068000468 Reorder the terms: 0.125 + r = 1.068000468 Solving 0.125 + r = 1.068000468 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + r = 1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = 1.068000468 + -0.125 r = 1.068000468 + -0.125 Combine like terms: 1.068000468 + -0.125 = 0.943000468 r = 0.943000468 Simplifying r = 0.943000468Subproblem 2
r + 0.125 = -1.068000468 Simplifying r + 0.125 = -1.068000468 Reorder the terms: 0.125 + r = -1.068000468 Solving 0.125 + r = -1.068000468 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + r = -1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = -1.068000468 + -0.125 r = -1.068000468 + -0.125 Combine like terms: -1.068000468 + -0.125 = -1.193000468 r = -1.193000468 Simplifying r = -1.193000468Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.943000468, -1.193000468}
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