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Simplifying r2 + -34r + 8 = 0 Reorder the terms: 8 + -34r + r2 = 0 Solving 8 + -34r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -34r + -8 + r2 = 0 + -8 Reorder the terms: 8 + -8 + -34r + r2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -34r + r2 = 0 + -8 -34r + r2 = 0 + -8 Combine like terms: 0 + -8 = -8 -34r + r2 = -8 The r term is -34r. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34r + 289 + r2 = -8 + 289 Reorder the terms: 289 + -34r + r2 = -8 + 289 Combine like terms: -8 + 289 = 281 289 + -34r + r2 = 281 Factor a perfect square on the left side: (r + -17)(r + -17) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (r + -17) equal to 16.763054614 and -16.763054614.Subproblem 1
r + -17 = 16.763054614 Simplifying r + -17 = 16.763054614 Reorder the terms: -17 + r = 16.763054614 Solving -17 + r = 16.763054614 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + r = 16.763054614 + 17 Combine like terms: -17 + 17 = 0 0 + r = 16.763054614 + 17 r = 16.763054614 + 17 Combine like terms: 16.763054614 + 17 = 33.763054614 r = 33.763054614 Simplifying r = 33.763054614Subproblem 2
r + -17 = -16.763054614 Simplifying r + -17 = -16.763054614 Reorder the terms: -17 + r = -16.763054614 Solving -17 + r = -16.763054614 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + r = -16.763054614 + 17 Combine like terms: -17 + 17 = 0 0 + r = -16.763054614 + 17 r = -16.763054614 + 17 Combine like terms: -16.763054614 + 17 = 0.236945386 r = 0.236945386 Simplifying r = 0.236945386Solution
The solution to the problem is based on the solutions from the subproblems. r = {33.763054614, 0.236945386}
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