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Simplifying r2 + 2r + -12 = 0 Reorder the terms: -12 + 2r + r2 = 0 Solving -12 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 2r + 12 + r2 = 0 + 12 Reorder the terms: -12 + 12 + 2r + r2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2r + r2 = 0 + 12 2r + r2 = 0 + 12 Combine like terms: 0 + 12 = 12 2r + r2 = 12 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 12 + 1 Reorder the terms: 1 + 2r + r2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2r + r2 = 13 Factor a perfect square on the left side: (r + 1)(r + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (r + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
r + 1 = 3.605551275 Simplifying r + 1 = 3.605551275 Reorder the terms: 1 + r = 3.605551275 Solving 1 + r = 3.605551275 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + r = 3.605551275 + -1 r = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 r = 2.605551275 Simplifying r = 2.605551275Subproblem 2
r + 1 = -3.605551275 Simplifying r + 1 = -3.605551275 Reorder the terms: 1 + r = -3.605551275 Solving 1 + r = -3.605551275 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + r = -3.605551275 + -1 r = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 r = -4.605551275 Simplifying r = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.605551275, -4.605551275}
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