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Simplifying 2r2 + -6r + -7 = 0 Reorder the terms: -7 + -6r + 2r2 = 0 Solving -7 + -6r + 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'. -3.5 + -3r + r2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3r + 3.5 + r2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3r + r2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3r + r2 = 0 + 3.5 -3r + r2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3r + r2 = 3.5 The r term is -3r. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3r + 2.25 + r2 = 3.5 + 2.25 Reorder the terms: 2.25 + -3r + r2 = 3.5 + 2.25 Combine like terms: 3.5 + 2.25 = 5.75 2.25 + -3r + r2 = 5.75 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (r + -1.5) equal to 2.397915762 and -2.397915762.Subproblem 1
r + -1.5 = 2.397915762 Simplifying r + -1.5 = 2.397915762 Reorder the terms: -1.5 + r = 2.397915762 Solving -1.5 + r = 2.397915762 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = 2.397915762 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 2.397915762 + 1.5 r = 2.397915762 + 1.5 Combine like terms: 2.397915762 + 1.5 = 3.897915762 r = 3.897915762 Simplifying r = 3.897915762Subproblem 2
r + -1.5 = -2.397915762 Simplifying r + -1.5 = -2.397915762 Reorder the terms: -1.5 + r = -2.397915762 Solving -1.5 + r = -2.397915762 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = -2.397915762 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -2.397915762 + 1.5 r = -2.397915762 + 1.5 Combine like terms: -2.397915762 + 1.5 = -0.897915762 r = -0.897915762 Simplifying r = -0.897915762Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.897915762, -0.897915762}
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