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Simplifying 2r2 + -7r + -16 = 0 Reorder the terms: -16 + -7r + 2r2 = 0 Solving -16 + -7r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -3.5r + r2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3.5r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + -3.5r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3.5r + r2 = 0 + 8 -3.5r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3.5r + r2 = 8 The r term is -3.5r. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5r + 3.0625 + r2 = 8 + 3.0625 Reorder the terms: 3.0625 + -3.5r + r2 = 8 + 3.0625 Combine like terms: 8 + 3.0625 = 11.0625 3.0625 + -3.5r + r2 = 11.0625 Factor a perfect square on the left side: (r + -1.75)(r + -1.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (r + -1.75) equal to 3.326033674 and -3.326033674.Subproblem 1
r + -1.75 = 3.326033674 Simplifying r + -1.75 = 3.326033674 Reorder the terms: -1.75 + r = 3.326033674 Solving -1.75 + r = 3.326033674 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + r = 3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + r = 3.326033674 + 1.75 r = 3.326033674 + 1.75 Combine like terms: 3.326033674 + 1.75 = 5.076033674 r = 5.076033674 Simplifying r = 5.076033674Subproblem 2
r + -1.75 = -3.326033674 Simplifying r + -1.75 = -3.326033674 Reorder the terms: -1.75 + r = -3.326033674 Solving -1.75 + r = -3.326033674 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + r = -3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + r = -3.326033674 + 1.75 r = -3.326033674 + 1.75 Combine like terms: -3.326033674 + 1.75 = -1.576033674 r = -1.576033674 Simplifying r = -1.576033674Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.076033674, -1.576033674}
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