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Simplifying r2 + -7r = 2 Reorder the terms: -7r + r2 = 2 Solving -7r + r2 = 2 Solving for variable 'r'. Reorder the terms: -2 + -7r + r2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -7r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -7r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -7r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7r + r2 = 0 + 2 -7r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7r + r2 = 2 The r term is -7r. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7r + 12.25 + r2 = 2 + 12.25 Reorder the terms: 12.25 + -7r + r2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + -7r + r2 = 14.25 Factor a perfect square on the left side: (r + -3.5)(r + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (r + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
r + -3.5 = 3.774917218 Simplifying r + -3.5 = 3.774917218 Reorder the terms: -3.5 + r = 3.774917218 Solving -3.5 + r = 3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 3.774917218 + 3.5 r = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 r = 7.274917218 Simplifying r = 7.274917218Subproblem 2
r + -3.5 = -3.774917218 Simplifying r + -3.5 = -3.774917218 Reorder the terms: -3.5 + r = -3.774917218 Solving -3.5 + r = -3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -3.774917218 + 3.5 r = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 r = -0.274917218 Simplifying r = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.274917218, -0.274917218}
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