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Simplifying r2 = -7r + 6 Reorder the terms: r2 = 6 + -7r Solving r2 = 6 + -7r Solving for variable 'r'. Reorder the terms: -6 + 7r + r2 = 6 + -7r + -6 + 7r Reorder the terms: -6 + 7r + r2 = 6 + -6 + -7r + 7r Combine like terms: 6 + -6 = 0 -6 + 7r + r2 = 0 + -7r + 7r -6 + 7r + r2 = -7r + 7r Combine like terms: -7r + 7r = 0 -6 + 7r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 7r + 6 + r2 = 0 + 6 Reorder the terms: -6 + 6 + 7r + r2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7r + r2 = 0 + 6 7r + r2 = 0 + 6 Combine like terms: 0 + 6 = 6 7r + r2 = 6 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 = 6 + 12.25 Reorder the terms: 12.25 + 7r + r2 = 6 + 12.25 Combine like terms: 6 + 12.25 = 18.25 12.25 + 7r + r2 = 18.25 Factor a perfect square on the left side: (r + 3.5)(r + 3.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (r + 3.5) equal to 4.272001873 and -4.272001873.Subproblem 1
r + 3.5 = 4.272001873 Simplifying r + 3.5 = 4.272001873 Reorder the terms: 3.5 + r = 4.272001873 Solving 3.5 + r = 4.272001873 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 = 4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = 4.272001873 + -3.5 r = 4.272001873 + -3.5 Combine like terms: 4.272001873 + -3.5 = 0.772001873 r = 0.772001873 Simplifying r = 0.772001873Subproblem 2
r + 3.5 = -4.272001873 Simplifying r + 3.5 = -4.272001873 Reorder the terms: 3.5 + r = -4.272001873 Solving 3.5 + r = -4.272001873 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 = -4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = -4.272001873 + -3.5 r = -4.272001873 + -3.5 Combine like terms: -4.272001873 + -3.5 = -7.772001873 r = -7.772001873 Simplifying r = -7.772001873Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.772001873, -7.772001873}
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