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Simplifying 5r2 + -33r + 50 = 0 Reorder the terms: 50 + -33r + 5r2 = 0 Solving 50 + -33r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 10 + -6.6r + r2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -6.6r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + -6.6r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -6.6r + r2 = 0 + -10 -6.6r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 -6.6r + r2 = -10 The r term is -6.6r. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6r + 10.89 + r2 = -10 + 10.89 Reorder the terms: 10.89 + -6.6r + r2 = -10 + 10.89 Combine like terms: -10 + 10.89 = 0.89 10.89 + -6.6r + r2 = 0.89 Factor a perfect square on the left side: (r + -3.3)(r + -3.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (r + -3.3) equal to 0.943398113 and -0.943398113.Subproblem 1
r + -3.3 = 0.943398113 Simplifying r + -3.3 = 0.943398113 Reorder the terms: -3.3 + r = 0.943398113 Solving -3.3 + r = 0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + r = 0.943398113 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + r = 0.943398113 + 3.3 r = 0.943398113 + 3.3 Combine like terms: 0.943398113 + 3.3 = 4.243398113 r = 4.243398113 Simplifying r = 4.243398113Subproblem 2
r + -3.3 = -0.943398113 Simplifying r + -3.3 = -0.943398113 Reorder the terms: -3.3 + r = -0.943398113 Solving -3.3 + r = -0.943398113 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + r = -0.943398113 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + r = -0.943398113 + 3.3 r = -0.943398113 + 3.3 Combine like terms: -0.943398113 + 3.3 = 2.356601887 r = 2.356601887 Simplifying r = 2.356601887Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.243398113, 2.356601887}
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