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Simplifying r2 + -4r = 98 Reorder the terms: -4r + r2 = 98 Solving -4r + r2 = 98 Solving for variable 'r'. Reorder the terms: -98 + -4r + r2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + -4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -4r + 98 + r2 = 0 + 98 Reorder the terms: -98 + 98 + -4r + r2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -4r + r2 = 0 + 98 -4r + r2 = 0 + 98 Combine like terms: 0 + 98 = 98 -4r + r2 = 98 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 98 + 4 Reorder the terms: 4 + -4r + r2 = 98 + 4 Combine like terms: 98 + 4 = 102 4 + -4r + r2 = 102 Factor a perfect square on the left side: (r + -2)(r + -2) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (r + -2) equal to 10.099504938 and -10.099504938.Subproblem 1
r + -2 = 10.099504938 Simplifying r + -2 = 10.099504938 Reorder the terms: -2 + r = 10.099504938 Solving -2 + r = 10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + r = 10.099504938 + 2 r = 10.099504938 + 2 Combine like terms: 10.099504938 + 2 = 12.099504938 r = 12.099504938 Simplifying r = 12.099504938Subproblem 2
r + -2 = -10.099504938 Simplifying r + -2 = -10.099504938 Reorder the terms: -2 + r = -10.099504938 Solving -2 + r = -10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + r = -10.099504938 + 2 r = -10.099504938 + 2 Combine like terms: -10.099504938 + 2 = -8.099504938 r = -8.099504938 Simplifying r = -8.099504938Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.099504938, -8.099504938}
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