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Simplifying r2 + 4r + -99 = 0 Reorder the terms: -99 + 4r + r2 = 0 Solving -99 + 4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 4r + 99 + r2 = 0 + 99 Reorder the terms: -99 + 99 + 4r + r2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 4r + r2 = 0 + 99 4r + r2 = 0 + 99 Combine like terms: 0 + 99 = 99 4r + r2 = 99 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 = 99 + 4 Reorder the terms: 4 + 4r + r2 = 99 + 4 Combine like terms: 99 + 4 = 103 4 + 4r + r2 = 103 Factor a perfect square on the left side: (r + 2)(r + 2) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (r + 2) equal to 10.148891565 and -10.148891565.Subproblem 1
r + 2 = 10.148891565 Simplifying r + 2 = 10.148891565 Reorder the terms: 2 + r = 10.148891565 Solving 2 + r = 10.148891565 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 = 10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + r = 10.148891565 + -2 r = 10.148891565 + -2 Combine like terms: 10.148891565 + -2 = 8.148891565 r = 8.148891565 Simplifying r = 8.148891565Subproblem 2
r + 2 = -10.148891565 Simplifying r + 2 = -10.148891565 Reorder the terms: 2 + r = -10.148891565 Solving 2 + r = -10.148891565 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 = -10.148891565 + -2 Combine like terms: 2 + -2 = 0 0 + r = -10.148891565 + -2 r = -10.148891565 + -2 Combine like terms: -10.148891565 + -2 = -12.148891565 r = -12.148891565 Simplifying r = -12.148891565Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.148891565, -12.148891565}
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