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Simplifying r2 + -40r + -112 = 0 Reorder the terms: -112 + -40r + r2 = 0 Solving -112 + -40r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -40r + 112 + r2 = 0 + 112 Reorder the terms: -112 + 112 + -40r + r2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -40r + r2 = 0 + 112 -40r + r2 = 0 + 112 Combine like terms: 0 + 112 = 112 -40r + r2 = 112 The r term is -40r. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40r + 400 + r2 = 112 + 400 Reorder the terms: 400 + -40r + r2 = 112 + 400 Combine like terms: 112 + 400 = 512 400 + -40r + r2 = 512 Factor a perfect square on the left side: (r + -20)(r + -20) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (r + -20) equal to 22.627416998 and -22.627416998.Subproblem 1
r + -20 = 22.627416998 Simplifying r + -20 = 22.627416998 Reorder the terms: -20 + r = 22.627416998 Solving -20 + r = 22.627416998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + r = 22.627416998 + 20 Combine like terms: -20 + 20 = 0 0 + r = 22.627416998 + 20 r = 22.627416998 + 20 Combine like terms: 22.627416998 + 20 = 42.627416998 r = 42.627416998 Simplifying r = 42.627416998Subproblem 2
r + -20 = -22.627416998 Simplifying r + -20 = -22.627416998 Reorder the terms: -20 + r = -22.627416998 Solving -20 + r = -22.627416998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + r = -22.627416998 + 20 Combine like terms: -20 + 20 = 0 0 + r = -22.627416998 + 20 r = -22.627416998 + 20 Combine like terms: -22.627416998 + 20 = -2.627416998 r = -2.627416998 Simplifying r = -2.627416998Solution
The solution to the problem is based on the solutions from the subproblems. r = {42.627416998, -2.627416998}
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