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Simplifying r2 + -10r = 7 Reorder the terms: -10r + r2 = 7 Solving -10r + r2 = 7 Solving for variable 'r'. Reorder the terms: -7 + -10r + r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -10r + 7 + r2 = 0 + 7 Reorder the terms: -7 + 7 + -10r + r2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10r + r2 = 0 + 7 -10r + r2 = 0 + 7 Combine like terms: 0 + 7 = 7 -10r + r2 = 7 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 = 7 + 25 Reorder the terms: 25 + -10r + r2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + -10r + r2 = 32 Factor a perfect square on the left side: (r + -5)(r + -5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (r + -5) equal to 5.656854249 and -5.656854249.Subproblem 1
r + -5 = 5.656854249 Simplifying r + -5 = 5.656854249 Reorder the terms: -5 + r = 5.656854249 Solving -5 + r = 5.656854249 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 = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + r = 5.656854249 + 5 r = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 r = 10.656854249 Simplifying r = 10.656854249Subproblem 2
r + -5 = -5.656854249 Simplifying r + -5 = -5.656854249 Reorder the terms: -5 + r = -5.656854249 Solving -5 + r = -5.656854249 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 = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + r = -5.656854249 + 5 r = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 r = -0.656854249 Simplifying r = -0.656854249Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.656854249, -0.656854249}
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