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Simplifying r2 + -20r + 42 = 0 Reorder the terms: 42 + -20r + r2 = 0 Solving 42 + -20r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -20r + -42 + r2 = 0 + -42 Reorder the terms: 42 + -42 + -20r + r2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -20r + r2 = 0 + -42 -20r + r2 = 0 + -42 Combine like terms: 0 + -42 = -42 -20r + r2 = -42 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 = -42 + 100 Reorder the terms: 100 + -20r + r2 = -42 + 100 Combine like terms: -42 + 100 = 58 100 + -20r + r2 = 58 Factor a perfect square on the left side: (r + -10)(r + -10) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (r + -10) equal to 7.615773106 and -7.615773106.Subproblem 1
r + -10 = 7.615773106 Simplifying r + -10 = 7.615773106 Reorder the terms: -10 + r = 7.615773106 Solving -10 + r = 7.615773106 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 = 7.615773106 + 10 Combine like terms: -10 + 10 = 0 0 + r = 7.615773106 + 10 r = 7.615773106 + 10 Combine like terms: 7.615773106 + 10 = 17.615773106 r = 17.615773106 Simplifying r = 17.615773106Subproblem 2
r + -10 = -7.615773106 Simplifying r + -10 = -7.615773106 Reorder the terms: -10 + r = -7.615773106 Solving -10 + r = -7.615773106 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 = -7.615773106 + 10 Combine like terms: -10 + 10 = 0 0 + r = -7.615773106 + 10 r = -7.615773106 + 10 Combine like terms: -7.615773106 + 10 = 2.384226894 r = 2.384226894 Simplifying r = 2.384226894Solution
The solution to the problem is based on the solutions from the subproblems. r = {17.615773106, 2.384226894}
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