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Simplifying 33.8 = r2 + 7.5r Reorder the terms: 33.8 = 7.5r + r2 Solving 33.8 = 7.5r + r2 Solving for variable 'r'. Reorder the terms: 33.8 + -7.5r + -1r2 = 7.5r + -7.5r + r2 + -1r2 Combine like terms: 7.5r + -7.5r = 0.0 33.8 + -7.5r + -1r2 = 0.0 + r2 + -1r2 33.8 + -7.5r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 33.8 + -7.5r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33.8 + 7.5r + r2 = 0 Move the constant term to the right: Add '33.8' to each side of the equation. -33.8 + 7.5r + 33.8 + r2 = 0 + 33.8 Reorder the terms: -33.8 + 33.8 + 7.5r + r2 = 0 + 33.8 Combine like terms: -33.8 + 33.8 = 0.0 0.0 + 7.5r + r2 = 0 + 33.8 7.5r + r2 = 0 + 33.8 Combine like terms: 0 + 33.8 = 33.8 7.5r + r2 = 33.8 The r term is 7.5r. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5r + 14.0625 + r2 = 33.8 + 14.0625 Reorder the terms: 14.0625 + 7.5r + r2 = 33.8 + 14.0625 Combine like terms: 33.8 + 14.0625 = 47.8625 14.0625 + 7.5r + r2 = 47.8625 Factor a perfect square on the left side: (r + 3.75)(r + 3.75) = 47.8625 Calculate the square root of the right side: 6.918272906 Break this problem into two subproblems by setting (r + 3.75) equal to 6.918272906 and -6.918272906.Subproblem 1
r + 3.75 = 6.918272906 Simplifying r + 3.75 = 6.918272906 Reorder the terms: 3.75 + r = 6.918272906 Solving 3.75 + r = 6.918272906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + r = 6.918272906 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + r = 6.918272906 + -3.75 r = 6.918272906 + -3.75 Combine like terms: 6.918272906 + -3.75 = 3.168272906 r = 3.168272906 Simplifying r = 3.168272906Subproblem 2
r + 3.75 = -6.918272906 Simplifying r + 3.75 = -6.918272906 Reorder the terms: 3.75 + r = -6.918272906 Solving 3.75 + r = -6.918272906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + r = -6.918272906 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + r = -6.918272906 + -3.75 r = -6.918272906 + -3.75 Combine like terms: -6.918272906 + -3.75 = -10.668272906 r = -10.668272906 Simplifying r = -10.668272906Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.168272906, -10.668272906}
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