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Simplifying r2 + -3r + -2 = 0 Reorder the terms: -2 + -3r + r2 = 0 Solving -2 + -3r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -3r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3r + r2 = 0 + 2 -3r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3r + r2 = 2 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 = 2 + 2.25 Reorder the terms: 2.25 + -3r + r2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3r + r2 = 4.25 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (r + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
r + -1.5 = 2.061552813 Simplifying r + -1.5 = 2.061552813 Reorder the terms: -1.5 + r = 2.061552813 Solving -1.5 + r = 2.061552813 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 = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 2.061552813 + 1.5 r = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 r = 3.561552813 Simplifying r = 3.561552813Subproblem 2
r + -1.5 = -2.061552813 Simplifying r + -1.5 = -2.061552813 Reorder the terms: -1.5 + r = -2.061552813 Solving -1.5 + r = -2.061552813 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 = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -2.061552813 + 1.5 r = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 r = -0.561552813 Simplifying r = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.561552813, -0.561552813}
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