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Simplifying 11r2 + -2r + -8 = 0 Reorder the terms: -8 + -2r + 11r2 = 0 Solving -8 + -2r + 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'. -0.7272727273 + -0.1818181818r + r2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.1818181818r + 0.7272727273 + r2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.1818181818r + r2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.1818181818r + r2 = 0 + 0.7272727273 -0.1818181818r + r2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.1818181818r + r2 = 0.7272727273 The r term is -0.1818181818r. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818r + 0.008264462808 + r2 = 0.7272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818r + r2 = 0.7272727273 + 0.008264462808 Combine like terms: 0.7272727273 + 0.008264462808 = 0.735537190108 0.008264462808 + -0.1818181818r + r2 = 0.735537190108 Factor a perfect square on the left side: (r + -0.0909090909)(r + -0.0909090909) = 0.735537190108 Calculate the square root of the right side: 0.857634648 Break this problem into two subproblems by setting (r + -0.0909090909) equal to 0.857634648 and -0.857634648.Subproblem 1
r + -0.0909090909 = 0.857634648 Simplifying r + -0.0909090909 = 0.857634648 Reorder the terms: -0.0909090909 + r = 0.857634648 Solving -0.0909090909 + r = 0.857634648 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + r = 0.857634648 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + r = 0.857634648 + 0.0909090909 r = 0.857634648 + 0.0909090909 Combine like terms: 0.857634648 + 0.0909090909 = 0.9485437389 r = 0.9485437389 Simplifying r = 0.9485437389Subproblem 2
r + -0.0909090909 = -0.857634648 Simplifying r + -0.0909090909 = -0.857634648 Reorder the terms: -0.0909090909 + r = -0.857634648 Solving -0.0909090909 + r = -0.857634648 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + r = -0.857634648 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + r = -0.857634648 + 0.0909090909 r = -0.857634648 + 0.0909090909 Combine like terms: -0.857634648 + 0.0909090909 = -0.7667255571 r = -0.7667255571 Simplifying r = -0.7667255571Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.9485437389, -0.7667255571}
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