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Simplifying 20r2 + 5r + -4 = 0 Reorder the terms: -4 + 5r + 20r2 = 0 Solving -4 + 5r + 20r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.2 + 0.25r + r2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.25r + 0.2 + r2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.25r + r2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.25r + r2 = 0 + 0.2 0.25r + r2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.25r + r2 = 0.2 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 = 0.2 + 0.015625 Reorder the terms: 0.015625 + 0.25r + r2 = 0.2 + 0.015625 Combine like terms: 0.2 + 0.015625 = 0.215625 0.015625 + 0.25r + r2 = 0.215625 Factor a perfect square on the left side: (r + 0.125)(r + 0.125) = 0.215625 Calculate the square root of the right side: 0.464354391 Break this problem into two subproblems by setting (r + 0.125) equal to 0.464354391 and -0.464354391.Subproblem 1
r + 0.125 = 0.464354391 Simplifying r + 0.125 = 0.464354391 Reorder the terms: 0.125 + r = 0.464354391 Solving 0.125 + r = 0.464354391 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 = 0.464354391 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = 0.464354391 + -0.125 r = 0.464354391 + -0.125 Combine like terms: 0.464354391 + -0.125 = 0.339354391 r = 0.339354391 Simplifying r = 0.339354391Subproblem 2
r + 0.125 = -0.464354391 Simplifying r + 0.125 = -0.464354391 Reorder the terms: 0.125 + r = -0.464354391 Solving 0.125 + r = -0.464354391 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 = -0.464354391 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = -0.464354391 + -0.125 r = -0.464354391 + -0.125 Combine like terms: -0.464354391 + -0.125 = -0.589354391 r = -0.589354391 Simplifying r = -0.589354391Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.339354391, -0.589354391}
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