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Simplifying r2 + 6r + -3 = 0 Reorder the terms: -3 + 6r + r2 = 0 Solving -3 + 6r + 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 + 6r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + 6r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6r + r2 = 0 + 3 6r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 6r + r2 = 3 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 3 + 9 Reorder the terms: 9 + 6r + r2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6r + r2 = 12 Factor a perfect square on the left side: (r + 3)(r + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
r + 3 = 3.464101615 Simplifying r + 3 = 3.464101615 Reorder the terms: 3 + r = 3.464101615 Solving 3 + r = 3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + r = 3.464101615 + -3 r = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 r = 0.464101615 Simplifying r = 0.464101615Subproblem 2
r + 3 = -3.464101615 Simplifying r + 3 = -3.464101615 Reorder the terms: 3 + r = -3.464101615 Solving 3 + r = -3.464101615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + r = -3.464101615 + -3 r = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 r = -6.464101615 Simplifying r = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.464101615, -6.464101615}
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