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Simplifying r2 + 12r + -64 = -52 Reorder the terms: -64 + 12r + r2 = -52 Solving -64 + 12r + r2 = -52 Solving for variable 'r'. Reorder the terms: -64 + 52 + 12r + r2 = -52 + 52 Combine like terms: -64 + 52 = -12 -12 + 12r + r2 = -52 + 52 Combine like terms: -52 + 52 = 0 -12 + 12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 12r + 12 + r2 = 0 + 12 Reorder the terms: -12 + 12 + 12r + r2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 12r + r2 = 0 + 12 12r + r2 = 0 + 12 Combine like terms: 0 + 12 = 12 12r + r2 = 12 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 = 12 + 36 Reorder the terms: 36 + 12r + r2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + 12r + r2 = 48 Factor a perfect square on the left side: (r + 6)(r + 6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (r + 6) equal to 6.92820323 and -6.92820323.Subproblem 1
r + 6 = 6.92820323 Simplifying r + 6 = 6.92820323 Reorder the terms: 6 + r = 6.92820323 Solving 6 + r = 6.92820323 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 = 6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + r = 6.92820323 + -6 r = 6.92820323 + -6 Combine like terms: 6.92820323 + -6 = 0.92820323 r = 0.92820323 Simplifying r = 0.92820323Subproblem 2
r + 6 = -6.92820323 Simplifying r + 6 = -6.92820323 Reorder the terms: 6 + r = -6.92820323 Solving 6 + r = -6.92820323 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 = -6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + r = -6.92820323 + -6 r = -6.92820323 + -6 Combine like terms: -6.92820323 + -6 = -12.92820323 r = -12.92820323 Simplifying r = -12.92820323Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.92820323, -12.92820323}
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