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Simplifying r2 + -44r + -35 = 0 Reorder the terms: -35 + -44r + r2 = 0 Solving -35 + -44r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -44r + 35 + r2 = 0 + 35 Reorder the terms: -35 + 35 + -44r + r2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -44r + r2 = 0 + 35 -44r + r2 = 0 + 35 Combine like terms: 0 + 35 = 35 -44r + r2 = 35 The r term is -44r. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44r + 484 + r2 = 35 + 484 Reorder the terms: 484 + -44r + r2 = 35 + 484 Combine like terms: 35 + 484 = 519 484 + -44r + r2 = 519 Factor a perfect square on the left side: (r + -22)(r + -22) = 519 Calculate the square root of the right side: 22.7815715 Break this problem into two subproblems by setting (r + -22) equal to 22.7815715 and -22.7815715.Subproblem 1
r + -22 = 22.7815715 Simplifying r + -22 = 22.7815715 Reorder the terms: -22 + r = 22.7815715 Solving -22 + r = 22.7815715 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + r = 22.7815715 + 22 Combine like terms: -22 + 22 = 0 0 + r = 22.7815715 + 22 r = 22.7815715 + 22 Combine like terms: 22.7815715 + 22 = 44.7815715 r = 44.7815715 Simplifying r = 44.7815715Subproblem 2
r + -22 = -22.7815715 Simplifying r + -22 = -22.7815715 Reorder the terms: -22 + r = -22.7815715 Solving -22 + r = -22.7815715 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + r = -22.7815715 + 22 Combine like terms: -22 + 22 = 0 0 + r = -22.7815715 + 22 r = -22.7815715 + 22 Combine like terms: -22.7815715 + 22 = -0.7815715 r = -0.7815715 Simplifying r = -0.7815715Solution
The solution to the problem is based on the solutions from the subproblems. r = {44.7815715, -0.7815715}
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