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Simplifying r2 + -14r + -10 = -3 Reorder the terms: -10 + -14r + r2 = -3 Solving -10 + -14r + r2 = -3 Solving for variable 'r'. Reorder the terms: -10 + 3 + -14r + r2 = -3 + 3 Combine like terms: -10 + 3 = -7 -7 + -14r + r2 = -3 + 3 Combine like terms: -3 + 3 = 0 -7 + -14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -14r + 7 + r2 = 0 + 7 Reorder the terms: -7 + 7 + -14r + r2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -14r + r2 = 0 + 7 -14r + r2 = 0 + 7 Combine like terms: 0 + 7 = 7 -14r + r2 = 7 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 = 7 + 49 Reorder the terms: 49 + -14r + r2 = 7 + 49 Combine like terms: 7 + 49 = 56 49 + -14r + r2 = 56 Factor a perfect square on the left side: (r + -7)(r + -7) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (r + -7) equal to 7.483314774 and -7.483314774.Subproblem 1
r + -7 = 7.483314774 Simplifying r + -7 = 7.483314774 Reorder the terms: -7 + r = 7.483314774 Solving -7 + r = 7.483314774 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 = 7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + r = 7.483314774 + 7 r = 7.483314774 + 7 Combine like terms: 7.483314774 + 7 = 14.483314774 r = 14.483314774 Simplifying r = 14.483314774Subproblem 2
r + -7 = -7.483314774 Simplifying r + -7 = -7.483314774 Reorder the terms: -7 + r = -7.483314774 Solving -7 + r = -7.483314774 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 = -7.483314774 + 7 Combine like terms: -7 + 7 = 0 0 + r = -7.483314774 + 7 r = -7.483314774 + 7 Combine like terms: -7.483314774 + 7 = -0.483314774 r = -0.483314774 Simplifying r = -0.483314774Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.483314774, -0.483314774}
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