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Simplifying 11r2 + 3r + -2 = 0 Reorder the terms: -2 + 3r + 11r2 = 0 Solving -2 + 3r + 11r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + 0.2727272727r + r2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.2727272727r + 0.1818181818 + r2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 0.2727272727r + r2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 0.2727272727r + r2 = 0 + 0.1818181818 0.2727272727r + r2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 0.2727272727r + r2 = 0.1818181818 The r term is 0.2727272727r. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727r + 0.01859504133 + r2 = 0.1818181818 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727r + r2 = 0.1818181818 + 0.01859504133 Combine like terms: 0.1818181818 + 0.01859504133 = 0.20041322313 0.01859504133 + 0.2727272727r + r2 = 0.20041322313 Factor a perfect square on the left side: (r + 0.1363636364)(r + 0.1363636364) = 0.20041322313 Calculate the square root of the right side: 0.447675355 Break this problem into two subproblems by setting (r + 0.1363636364) equal to 0.447675355 and -0.447675355.Subproblem 1
r + 0.1363636364 = 0.447675355 Simplifying r + 0.1363636364 = 0.447675355 Reorder the terms: 0.1363636364 + r = 0.447675355 Solving 0.1363636364 + r = 0.447675355 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + r = 0.447675355 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + r = 0.447675355 + -0.1363636364 r = 0.447675355 + -0.1363636364 Combine like terms: 0.447675355 + -0.1363636364 = 0.3113117186 r = 0.3113117186 Simplifying r = 0.3113117186Subproblem 2
r + 0.1363636364 = -0.447675355 Simplifying r + 0.1363636364 = -0.447675355 Reorder the terms: 0.1363636364 + r = -0.447675355 Solving 0.1363636364 + r = -0.447675355 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + r = -0.447675355 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + r = -0.447675355 + -0.1363636364 r = -0.447675355 + -0.1363636364 Combine like terms: -0.447675355 + -0.1363636364 = -0.5840389914 r = -0.5840389914 Simplifying r = -0.5840389914Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.3113117186, -0.5840389914}
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