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Simplifying r2 + 4r + -68 = -4 Reorder the terms: -68 + 4r + r2 = -4 Solving -68 + 4r + r2 = -4 Solving for variable 'r'. Reorder the terms: -68 + 4 + 4r + r2 = -4 + 4 Combine like terms: -68 + 4 = -64 -64 + 4r + r2 = -4 + 4 Combine like terms: -4 + 4 = 0 -64 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 4r + 64 + r2 = 0 + 64 Reorder the terms: -64 + 64 + 4r + r2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 4r + r2 = 0 + 64 4r + r2 = 0 + 64 Combine like terms: 0 + 64 = 64 4r + r2 = 64 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 = 64 + 4 Reorder the terms: 4 + 4r + r2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + 4r + r2 = 68 Factor a perfect square on the left side: (r + 2)(r + 2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (r + 2) equal to 8.246211251 and -8.246211251.Subproblem 1
r + 2 = 8.246211251 Simplifying r + 2 = 8.246211251 Reorder the terms: 2 + r = 8.246211251 Solving 2 + r = 8.246211251 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 = 8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + r = 8.246211251 + -2 r = 8.246211251 + -2 Combine like terms: 8.246211251 + -2 = 6.246211251 r = 6.246211251 Simplifying r = 6.246211251Subproblem 2
r + 2 = -8.246211251 Simplifying r + 2 = -8.246211251 Reorder the terms: 2 + r = -8.246211251 Solving 2 + r = -8.246211251 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 = -8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + r = -8.246211251 + -2 r = -8.246211251 + -2 Combine like terms: -8.246211251 + -2 = -10.246211251 r = -10.246211251 Simplifying r = -10.246211251Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.246211251, -10.246211251}
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