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Simplifying r2 + -20r + 74 = -4 Reorder the terms: 74 + -20r + r2 = -4 Solving 74 + -20r + r2 = -4 Solving for variable 'r'. Reorder the terms: 74 + 4 + -20r + r2 = -4 + 4 Combine like terms: 74 + 4 = 78 78 + -20r + r2 = -4 + 4 Combine like terms: -4 + 4 = 0 78 + -20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-78' to each side of the equation. 78 + -20r + -78 + r2 = 0 + -78 Reorder the terms: 78 + -78 + -20r + r2 = 0 + -78 Combine like terms: 78 + -78 = 0 0 + -20r + r2 = 0 + -78 -20r + r2 = 0 + -78 Combine like terms: 0 + -78 = -78 -20r + r2 = -78 The r term is -20r. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20r + 100 + r2 = -78 + 100 Reorder the terms: 100 + -20r + r2 = -78 + 100 Combine like terms: -78 + 100 = 22 100 + -20r + r2 = 22 Factor a perfect square on the left side: (r + -10)(r + -10) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (r + -10) equal to 4.69041576 and -4.69041576.Subproblem 1
r + -10 = 4.69041576 Simplifying r + -10 = 4.69041576 Reorder the terms: -10 + r = 4.69041576 Solving -10 + r = 4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 4.69041576 + 10 Combine like terms: -10 + 10 = 0 0 + r = 4.69041576 + 10 r = 4.69041576 + 10 Combine like terms: 4.69041576 + 10 = 14.69041576 r = 14.69041576 Simplifying r = 14.69041576Subproblem 2
r + -10 = -4.69041576 Simplifying r + -10 = -4.69041576 Reorder the terms: -10 + r = -4.69041576 Solving -10 + r = -4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -4.69041576 + 10 Combine like terms: -10 + 10 = 0 0 + r = -4.69041576 + 10 r = -4.69041576 + 10 Combine like terms: -4.69041576 + 10 = 5.30958424 r = 5.30958424 Simplifying r = 5.30958424Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.69041576, 5.30958424}
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