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Simplifying r2 + 20r + -47 = 0 Reorder the terms: -47 + 20r + r2 = 0 Solving -47 + 20r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 20r + 47 + r2 = 0 + 47 Reorder the terms: -47 + 47 + 20r + r2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 20r + r2 = 0 + 47 20r + r2 = 0 + 47 Combine like terms: 0 + 47 = 47 20r + r2 = 47 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 = 47 + 100 Reorder the terms: 100 + 20r + r2 = 47 + 100 Combine like terms: 47 + 100 = 147 100 + 20r + r2 = 147 Factor a perfect square on the left side: (r + 10)(r + 10) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (r + 10) equal to 12.124355653 and -12.124355653.Subproblem 1
r + 10 = 12.124355653 Simplifying r + 10 = 12.124355653 Reorder the terms: 10 + r = 12.124355653 Solving 10 + r = 12.124355653 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 = 12.124355653 + -10 Combine like terms: 10 + -10 = 0 0 + r = 12.124355653 + -10 r = 12.124355653 + -10 Combine like terms: 12.124355653 + -10 = 2.124355653 r = 2.124355653 Simplifying r = 2.124355653Subproblem 2
r + 10 = -12.124355653 Simplifying r + 10 = -12.124355653 Reorder the terms: 10 + r = -12.124355653 Solving 10 + r = -12.124355653 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 = -12.124355653 + -10 Combine like terms: 10 + -10 = 0 0 + r = -12.124355653 + -10 r = -12.124355653 + -10 Combine like terms: -12.124355653 + -10 = -22.124355653 r = -22.124355653 Simplifying r = -22.124355653Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.124355653, -22.124355653}
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