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Simplifying r2 + 20r + -4 = 0 Reorder the terms: -4 + 20r + r2 = 0 Solving -4 + 20r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 20r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + 20r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 20r + r2 = 0 + 4 20r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 20r + r2 = 4 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 = 4 + 100 Reorder the terms: 100 + 20r + r2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + 20r + r2 = 104 Factor a perfect square on the left side: (r + 10)(r + 10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (r + 10) equal to 10.198039027 and -10.198039027.Subproblem 1
r + 10 = 10.198039027 Simplifying r + 10 = 10.198039027 Reorder the terms: 10 + r = 10.198039027 Solving 10 + r = 10.198039027 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 = 10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + r = 10.198039027 + -10 r = 10.198039027 + -10 Combine like terms: 10.198039027 + -10 = 0.198039027 r = 0.198039027 Simplifying r = 0.198039027Subproblem 2
r + 10 = -10.198039027 Simplifying r + 10 = -10.198039027 Reorder the terms: 10 + r = -10.198039027 Solving 10 + r = -10.198039027 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 = -10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + r = -10.198039027 + -10 r = -10.198039027 + -10 Combine like terms: -10.198039027 + -10 = -20.198039027 r = -20.198039027 Simplifying r = -20.198039027Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.198039027, -20.198039027}
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