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Simplifying r2 + -14r + 10 = 0 Reorder the terms: 10 + -14r + r2 = 0 Solving 10 + -14r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -14r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + -14r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14r + r2 = 0 + -10 -14r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14r + r2 = -10 The r term is -14r. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14r + 49 + r2 = -10 + 49 Reorder the terms: 49 + -14r + r2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + -14r + r2 = 39 Factor a perfect square on the left side: (r + -7)(r + -7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (r + -7) equal to 6.244997998 and -6.244997998.Subproblem 1
r + -7 = 6.244997998 Simplifying r + -7 = 6.244997998 Reorder the terms: -7 + r = 6.244997998 Solving -7 + r = 6.244997998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = 6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + r = 6.244997998 + 7 r = 6.244997998 + 7 Combine like terms: 6.244997998 + 7 = 13.244997998 r = 13.244997998 Simplifying r = 13.244997998Subproblem 2
r + -7 = -6.244997998 Simplifying r + -7 = -6.244997998 Reorder the terms: -7 + r = -6.244997998 Solving -7 + r = -6.244997998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = -6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + r = -6.244997998 + 7 r = -6.244997998 + 7 Combine like terms: -6.244997998 + 7 = 0.755002002 r = 0.755002002 Simplifying r = 0.755002002Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.244997998, 0.755002002}
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