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Simplifying r2 + -4r + -91 = 0 Reorder the terms: -91 + -4r + r2 = 0 Solving -91 + -4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + -4r + 91 + r2 = 0 + 91 Reorder the terms: -91 + 91 + -4r + r2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + -4r + r2 = 0 + 91 -4r + r2 = 0 + 91 Combine like terms: 0 + 91 = 91 -4r + r2 = 91 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 = 91 + 4 Reorder the terms: 4 + -4r + r2 = 91 + 4 Combine like terms: 91 + 4 = 95 4 + -4r + r2 = 95 Factor a perfect square on the left side: (r + -2)(r + -2) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (r + -2) equal to 9.746794345 and -9.746794345.Subproblem 1
r + -2 = 9.746794345 Simplifying r + -2 = 9.746794345 Reorder the terms: -2 + r = 9.746794345 Solving -2 + r = 9.746794345 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 = 9.746794345 + 2 Combine like terms: -2 + 2 = 0 0 + r = 9.746794345 + 2 r = 9.746794345 + 2 Combine like terms: 9.746794345 + 2 = 11.746794345 r = 11.746794345 Simplifying r = 11.746794345Subproblem 2
r + -2 = -9.746794345 Simplifying r + -2 = -9.746794345 Reorder the terms: -2 + r = -9.746794345 Solving -2 + r = -9.746794345 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 = -9.746794345 + 2 Combine like terms: -2 + 2 = 0 0 + r = -9.746794345 + 2 r = -9.746794345 + 2 Combine like terms: -9.746794345 + 2 = -7.746794345 r = -7.746794345 Simplifying r = -7.746794345Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.746794345, -7.746794345}
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