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Simplifying r2 + 12r + -128 = 0 Reorder the terms: -128 + 12r + r2 = 0 Solving -128 + 12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 12r + 128 + r2 = 0 + 128 Reorder the terms: -128 + 128 + 12r + r2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 12r + r2 = 0 + 128 12r + r2 = 0 + 128 Combine like terms: 0 + 128 = 128 12r + r2 = 128 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 128 + 36 Reorder the terms: 36 + 12r + r2 = 128 + 36 Combine like terms: 128 + 36 = 164 36 + 12r + r2 = 164 Factor a perfect square on the left side: (r + 6)(r + 6) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (r + 6) equal to 12.806248475 and -12.806248475.Subproblem 1
r + 6 = 12.806248475 Simplifying r + 6 = 12.806248475 Reorder the terms: 6 + r = 12.806248475 Solving 6 + r = 12.806248475 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 12.806248475 + -6 Combine like terms: 6 + -6 = 0 0 + r = 12.806248475 + -6 r = 12.806248475 + -6 Combine like terms: 12.806248475 + -6 = 6.806248475 r = 6.806248475 Simplifying r = 6.806248475Subproblem 2
r + 6 = -12.806248475 Simplifying r + 6 = -12.806248475 Reorder the terms: 6 + r = -12.806248475 Solving 6 + r = -12.806248475 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -12.806248475 + -6 Combine like terms: 6 + -6 = 0 0 + r = -12.806248475 + -6 r = -12.806248475 + -6 Combine like terms: -12.806248475 + -6 = -18.806248475 r = -18.806248475 Simplifying r = -18.806248475Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.806248475, -18.806248475}
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