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Simplifying r2 + -14r + -98 = -2 Reorder the terms: -98 + -14r + r2 = -2 Solving -98 + -14r + r2 = -2 Solving for variable 'r'. Reorder the terms: -98 + 2 + -14r + r2 = -2 + 2 Combine like terms: -98 + 2 = -96 -96 + -14r + r2 = -2 + 2 Combine like terms: -2 + 2 = 0 -96 + -14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -14r + 96 + r2 = 0 + 96 Reorder the terms: -96 + 96 + -14r + r2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -14r + r2 = 0 + 96 -14r + r2 = 0 + 96 Combine like terms: 0 + 96 = 96 -14r + r2 = 96 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 = 96 + 49 Reorder the terms: 49 + -14r + r2 = 96 + 49 Combine like terms: 96 + 49 = 145 49 + -14r + r2 = 145 Factor a perfect square on the left side: (r + -7)(r + -7) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (r + -7) equal to 12.041594579 and -12.041594579.Subproblem 1
r + -7 = 12.041594579 Simplifying r + -7 = 12.041594579 Reorder the terms: -7 + r = 12.041594579 Solving -7 + r = 12.041594579 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 = 12.041594579 + 7 Combine like terms: -7 + 7 = 0 0 + r = 12.041594579 + 7 r = 12.041594579 + 7 Combine like terms: 12.041594579 + 7 = 19.041594579 r = 19.041594579 Simplifying r = 19.041594579Subproblem 2
r + -7 = -12.041594579 Simplifying r + -7 = -12.041594579 Reorder the terms: -7 + r = -12.041594579 Solving -7 + r = -12.041594579 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 = -12.041594579 + 7 Combine like terms: -7 + 7 = 0 0 + r = -12.041594579 + 7 r = -12.041594579 + 7 Combine like terms: -12.041594579 + 7 = -5.041594579 r = -5.041594579 Simplifying r = -5.041594579Solution
The solution to the problem is based on the solutions from the subproblems. r = {19.041594579, -5.041594579}
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