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Simplifying r2 + 8r + -10 = 0 Reorder the terms: -10 + 8r + r2 = 0 Solving -10 + 8r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 8r + 10 + r2 = 0 + 10 Reorder the terms: -10 + 10 + 8r + r2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 8r + r2 = 0 + 10 8r + r2 = 0 + 10 Combine like terms: 0 + 10 = 10 8r + r2 = 10 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 = 10 + 16 Reorder the terms: 16 + 8r + r2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + 8r + r2 = 26 Factor a perfect square on the left side: (r + 4)(r + 4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (r + 4) equal to 5.099019514 and -5.099019514.Subproblem 1
r + 4 = 5.099019514 Simplifying r + 4 = 5.099019514 Reorder the terms: 4 + r = 5.099019514 Solving 4 + r = 5.099019514 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 = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + r = 5.099019514 + -4 r = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 r = 1.099019514 Simplifying r = 1.099019514Subproblem 2
r + 4 = -5.099019514 Simplifying r + 4 = -5.099019514 Reorder the terms: 4 + r = -5.099019514 Solving 4 + r = -5.099019514 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 = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + r = -5.099019514 + -4 r = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 r = -9.099019514 Simplifying r = -9.099019514Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.099019514, -9.099019514}
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