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Simplifying r2 + 16r + -45 = 0 Reorder the terms: -45 + 16r + r2 = 0 Solving -45 + 16r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 16r + 45 + r2 = 0 + 45 Reorder the terms: -45 + 45 + 16r + r2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 16r + r2 = 0 + 45 16r + r2 = 0 + 45 Combine like terms: 0 + 45 = 45 16r + r2 = 45 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = 45 + 64 Reorder the terms: 64 + 16r + r2 = 45 + 64 Combine like terms: 45 + 64 = 109 64 + 16r + r2 = 109 Factor a perfect square on the left side: (r + 8)(r + 8) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (r + 8) equal to 10.440306509 and -10.440306509.Subproblem 1
r + 8 = 10.440306509 Simplifying r + 8 = 10.440306509 Reorder the terms: 8 + r = 10.440306509 Solving 8 + r = 10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 10.440306509 + -8 Combine like terms: 8 + -8 = 0 0 + r = 10.440306509 + -8 r = 10.440306509 + -8 Combine like terms: 10.440306509 + -8 = 2.440306509 r = 2.440306509 Simplifying r = 2.440306509Subproblem 2
r + 8 = -10.440306509 Simplifying r + 8 = -10.440306509 Reorder the terms: 8 + r = -10.440306509 Solving 8 + r = -10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -10.440306509 + -8 Combine like terms: 8 + -8 = 0 0 + r = -10.440306509 + -8 r = -10.440306509 + -8 Combine like terms: -10.440306509 + -8 = -18.440306509 r = -18.440306509 Simplifying r = -18.440306509Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.440306509, -18.440306509}
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