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Simplifying 3 + -1r2 + -8r + 16 = 0 Reorder the terms: 3 + 16 + -8r + -1r2 = 0 Combine like terms: 3 + 16 = 19 19 + -8r + -1r2 = 0 Solving 19 + -8r + -1r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 8r + r2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 8r + 19 + r2 = 0 + 19 Reorder the terms: -19 + 19 + 8r + r2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 8r + r2 = 0 + 19 8r + r2 = 0 + 19 Combine like terms: 0 + 19 = 19 8r + r2 = 19 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 19 + 16 Reorder the terms: 16 + 8r + r2 = 19 + 16 Combine like terms: 19 + 16 = 35 16 + 8r + r2 = 35 Factor a perfect square on the left side: (r + 4)(r + 4) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (r + 4) equal to 5.916079783 and -5.916079783.Subproblem 1
r + 4 = 5.916079783 Simplifying r + 4 = 5.916079783 Reorder the terms: 4 + r = 5.916079783 Solving 4 + r = 5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + r = 5.916079783 + -4 r = 5.916079783 + -4 Combine like terms: 5.916079783 + -4 = 1.916079783 r = 1.916079783 Simplifying r = 1.916079783Subproblem 2
r + 4 = -5.916079783 Simplifying r + 4 = -5.916079783 Reorder the terms: 4 + r = -5.916079783 Solving 4 + r = -5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + r = -5.916079783 + -4 r = -5.916079783 + -4 Combine like terms: -5.916079783 + -4 = -9.916079783 r = -9.916079783 Simplifying r = -9.916079783Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.916079783, -9.916079783}
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