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Simplifying r2 + 10r + 3 = 0 Reorder the terms: 3 + 10r + r2 = 0 Solving 3 + 10r + 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 + 10r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + 10r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10r + r2 = 0 + -3 10r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 10r + r2 = -3 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = -3 + 25 Reorder the terms: 25 + 10r + r2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + 10r + r2 = 22 Factor a perfect square on the left side: (r + 5)(r + 5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (r + 5) equal to 4.69041576 and -4.69041576.Subproblem 1
r + 5 = 4.69041576 Simplifying r + 5 = 4.69041576 Reorder the terms: 5 + r = 4.69041576 Solving 5 + r = 4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + r = 4.69041576 + -5 r = 4.69041576 + -5 Combine like terms: 4.69041576 + -5 = -0.30958424 r = -0.30958424 Simplifying r = -0.30958424Subproblem 2
r + 5 = -4.69041576 Simplifying r + 5 = -4.69041576 Reorder the terms: 5 + r = -4.69041576 Solving 5 + r = -4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + r = -4.69041576 + -5 r = -4.69041576 + -5 Combine like terms: -4.69041576 + -5 = -9.69041576 r = -9.69041576 Simplifying r = -9.69041576Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.30958424, -9.69041576}
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