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Simplifying r2 + -3r + -8 = 0 Reorder the terms: -8 + -3r + r2 = 0 Solving -8 + -3r + 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 + -3r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + -3r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3r + r2 = 0 + 8 -3r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3r + r2 = 8 The r term is -3r. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3r + 2.25 + r2 = 8 + 2.25 Reorder the terms: 2.25 + -3r + r2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3r + r2 = 10.25 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (r + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
r + -1.5 = 3.201562119 Simplifying r + -1.5 = 3.201562119 Reorder the terms: -1.5 + r = 3.201562119 Solving -1.5 + r = 3.201562119 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 3.201562119 + 1.5 r = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 r = 4.701562119 Simplifying r = 4.701562119Subproblem 2
r + -1.5 = -3.201562119 Simplifying r + -1.5 = -3.201562119 Reorder the terms: -1.5 + r = -3.201562119 Solving -1.5 + r = -3.201562119 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -3.201562119 + 1.5 r = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 r = -1.701562119 Simplifying r = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.701562119, -1.701562119}
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