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Simplifying r2 + -8r + 3 = 0 Reorder the terms: 3 + -8r + r2 = 0 Solving 3 + -8r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + -8r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8r + r2 = 0 + -3 -8r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8r + r2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8r + r2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8r + r2 = 13 Factor a perfect square on the left side: (r + -4)(r + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (r + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
r + -4 = 3.605551275 Simplifying r + -4 = 3.605551275 Reorder the terms: -4 + r = 3.605551275 Solving -4 + r = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + r = 3.605551275 + 4 r = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 r = 7.605551275 Simplifying r = 7.605551275Subproblem 2
r + -4 = -3.605551275 Simplifying r + -4 = -3.605551275 Reorder the terms: -4 + r = -3.605551275 Solving -4 + r = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + r = -3.605551275 + 4 r = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 r = 0.394448725 Simplifying r = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.605551275, 0.394448725}
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