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Simplifying 4r2 + -1r + -1 = 0 Reorder the terms: -1 + -1r + 4r2 = 0 Solving -1 + -1r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -0.25r + r2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.25r + 0.25 + r2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.25r + r2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.25r + r2 = 0 + 0.25 -0.25r + r2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.25r + r2 = 0.25 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 = 0.25 + 0.015625 Reorder the terms: 0.015625 + -0.25r + r2 = 0.25 + 0.015625 Combine like terms: 0.25 + 0.015625 = 0.265625 0.015625 + -0.25r + r2 = 0.265625 Factor a perfect square on the left side: (r + -0.125)(r + -0.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (r + -0.125) equal to 0.515388203 and -0.515388203.Subproblem 1
r + -0.125 = 0.515388203 Simplifying r + -0.125 = 0.515388203 Reorder the terms: -0.125 + r = 0.515388203 Solving -0.125 + r = 0.515388203 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 = 0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = 0.515388203 + 0.125 r = 0.515388203 + 0.125 Combine like terms: 0.515388203 + 0.125 = 0.640388203 r = 0.640388203 Simplifying r = 0.640388203Subproblem 2
r + -0.125 = -0.515388203 Simplifying r + -0.125 = -0.515388203 Reorder the terms: -0.125 + r = -0.515388203 Solving -0.125 + r = -0.515388203 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 = -0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = -0.515388203 + 0.125 r = -0.515388203 + 0.125 Combine like terms: -0.515388203 + 0.125 = -0.390388203 r = -0.390388203 Simplifying r = -0.390388203Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.640388203, -0.390388203}
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