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Simplifying 55r2 + -39r + -8 = 0 Reorder the terms: -8 + -39r + 55r2 = 0 Solving -8 + -39r + 55r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. -0.1454545455 + -0.7090909091r + r2 = 0 Move the constant term to the right: Add '0.1454545455' to each side of the equation. -0.1454545455 + -0.7090909091r + 0.1454545455 + r2 = 0 + 0.1454545455 Reorder the terms: -0.1454545455 + 0.1454545455 + -0.7090909091r + r2 = 0 + 0.1454545455 Combine like terms: -0.1454545455 + 0.1454545455 = 0.0000000000 0.0000000000 + -0.7090909091r + r2 = 0 + 0.1454545455 -0.7090909091r + r2 = 0 + 0.1454545455 Combine like terms: 0 + 0.1454545455 = 0.1454545455 -0.7090909091r + r2 = 0.1454545455 The r term is -0.7090909091r. Take half its coefficient (-0.3545454546). Square it (0.1257024794) and add it to both sides. Add '0.1257024794' to each side of the equation. -0.7090909091r + 0.1257024794 + r2 = 0.1454545455 + 0.1257024794 Reorder the terms: 0.1257024794 + -0.7090909091r + r2 = 0.1454545455 + 0.1257024794 Combine like terms: 0.1454545455 + 0.1257024794 = 0.2711570249 0.1257024794 + -0.7090909091r + r2 = 0.2711570249 Factor a perfect square on the left side: (r + -0.3545454546)(r + -0.3545454546) = 0.2711570249 Calculate the square root of the right side: 0.5207274 Break this problem into two subproblems by setting (r + -0.3545454546) equal to 0.5207274 and -0.5207274.Subproblem 1
r + -0.3545454546 = 0.5207274 Simplifying r + -0.3545454546 = 0.5207274 Reorder the terms: -0.3545454546 + r = 0.5207274 Solving -0.3545454546 + r = 0.5207274 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3545454546' to each side of the equation. -0.3545454546 + 0.3545454546 + r = 0.5207274 + 0.3545454546 Combine like terms: -0.3545454546 + 0.3545454546 = 0.0000000000 0.0000000000 + r = 0.5207274 + 0.3545454546 r = 0.5207274 + 0.3545454546 Combine like terms: 0.5207274 + 0.3545454546 = 0.8752728546 r = 0.8752728546 Simplifying r = 0.8752728546Subproblem 2
r + -0.3545454546 = -0.5207274 Simplifying r + -0.3545454546 = -0.5207274 Reorder the terms: -0.3545454546 + r = -0.5207274 Solving -0.3545454546 + r = -0.5207274 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3545454546' to each side of the equation. -0.3545454546 + 0.3545454546 + r = -0.5207274 + 0.3545454546 Combine like terms: -0.3545454546 + 0.3545454546 = 0.0000000000 0.0000000000 + r = -0.5207274 + 0.3545454546 r = -0.5207274 + 0.3545454546 Combine like terms: -0.5207274 + 0.3545454546 = -0.1661819454 r = -0.1661819454 Simplifying r = -0.1661819454Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.8752728546, -0.1661819454}
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