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Simplifying -1r2 + 7r + -8 = 0 Reorder the terms: -8 + 7r + -1r2 = 0 Solving -8 + 7r + -1r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -7r + r2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7r + -8 + r2 = 0 + -8 Reorder the terms: 8 + -8 + -7r + r2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7r + r2 = 0 + -8 -7r + r2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7r + r2 = -8 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 = -8 + 12.25 Reorder the terms: 12.25 + -7r + r2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7r + r2 = 4.25 Factor a perfect square on the left side: (r + -3.5)(r + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (r + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
r + -3.5 = 2.061552813 Simplifying r + -3.5 = 2.061552813 Reorder the terms: -3.5 + r = 2.061552813 Solving -3.5 + r = 2.061552813 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 = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 2.061552813 + 3.5 r = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 r = 5.561552813 Simplifying r = 5.561552813Subproblem 2
r + -3.5 = -2.061552813 Simplifying r + -3.5 = -2.061552813 Reorder the terms: -3.5 + r = -2.061552813 Solving -3.5 + r = -2.061552813 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 = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -2.061552813 + 3.5 r = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 r = 1.438447187 Simplifying r = 1.438447187Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.561552813, 1.438447187}
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