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Simplifying 2r2 + 8r + -33 = 0 Reorder the terms: -33 + 8r + 2r2 = 0 Solving -33 + 8r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 4r + r2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 4r + 16.5 + r2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 4r + r2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 4r + r2 = 0 + 16.5 4r + r2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 4r + r2 = 16.5 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 16.5 + 4 Reorder the terms: 4 + 4r + r2 = 16.5 + 4 Combine like terms: 16.5 + 4 = 20.5 4 + 4r + r2 = 20.5 Factor a perfect square on the left side: (r + 2)(r + 2) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (r + 2) equal to 4.527692569 and -4.527692569.Subproblem 1
r + 2 = 4.527692569 Simplifying r + 2 = 4.527692569 Reorder the terms: 2 + r = 4.527692569 Solving 2 + r = 4.527692569 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 4.527692569 + -2 Combine like terms: 2 + -2 = 0 0 + r = 4.527692569 + -2 r = 4.527692569 + -2 Combine like terms: 4.527692569 + -2 = 2.527692569 r = 2.527692569 Simplifying r = 2.527692569Subproblem 2
r + 2 = -4.527692569 Simplifying r + 2 = -4.527692569 Reorder the terms: 2 + r = -4.527692569 Solving 2 + r = -4.527692569 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -4.527692569 + -2 Combine like terms: 2 + -2 = 0 0 + r = -4.527692569 + -2 r = -4.527692569 + -2 Combine like terms: -4.527692569 + -2 = -6.527692569 r = -6.527692569 Simplifying r = -6.527692569Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.527692569, -6.527692569}
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