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Simplifying r2 + 6r + -25 = 0 Reorder the terms: -25 + 6r + r2 = 0 Solving -25 + 6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 6r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + 6r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 6r + r2 = 0 + 25 6r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 6r + r2 = 25 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 = 25 + 9 Reorder the terms: 9 + 6r + r2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + 6r + r2 = 34 Factor a perfect square on the left side: (r + 3)(r + 3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (r + 3) equal to 5.830951895 and -5.830951895.Subproblem 1
r + 3 = 5.830951895 Simplifying r + 3 = 5.830951895 Reorder the terms: 3 + r = 5.830951895 Solving 3 + r = 5.830951895 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 = 5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + r = 5.830951895 + -3 r = 5.830951895 + -3 Combine like terms: 5.830951895 + -3 = 2.830951895 r = 2.830951895 Simplifying r = 2.830951895Subproblem 2
r + 3 = -5.830951895 Simplifying r + 3 = -5.830951895 Reorder the terms: 3 + r = -5.830951895 Solving 3 + r = -5.830951895 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 = -5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + r = -5.830951895 + -3 r = -5.830951895 + -3 Combine like terms: -5.830951895 + -3 = -8.830951895 r = -8.830951895 Simplifying r = -8.830951895Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.830951895, -8.830951895}
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