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Simplifying r2 + 8r + -35 = 0 Reorder the terms: -35 + 8r + r2 = 0 Solving -35 + 8r + 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 + 8r + 35 + r2 = 0 + 35 Reorder the terms: -35 + 35 + 8r + r2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 8r + r2 = 0 + 35 8r + r2 = 0 + 35 Combine like terms: 0 + 35 = 35 8r + r2 = 35 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 35 + 16 Reorder the terms: 16 + 8r + r2 = 35 + 16 Combine like terms: 35 + 16 = 51 16 + 8r + r2 = 51 Factor a perfect square on the left side: (r + 4)(r + 4) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (r + 4) equal to 7.141428429 and -7.141428429.Subproblem 1
r + 4 = 7.141428429 Simplifying r + 4 = 7.141428429 Reorder the terms: 4 + r = 7.141428429 Solving 4 + r = 7.141428429 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 7.141428429 + -4 Combine like terms: 4 + -4 = 0 0 + r = 7.141428429 + -4 r = 7.141428429 + -4 Combine like terms: 7.141428429 + -4 = 3.141428429 r = 3.141428429 Simplifying r = 3.141428429Subproblem 2
r + 4 = -7.141428429 Simplifying r + 4 = -7.141428429 Reorder the terms: 4 + r = -7.141428429 Solving 4 + r = -7.141428429 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -7.141428429 + -4 Combine like terms: 4 + -4 = 0 0 + r = -7.141428429 + -4 r = -7.141428429 + -4 Combine like terms: -7.141428429 + -4 = -11.141428429 r = -11.141428429 Simplifying r = -11.141428429Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.141428429, -11.141428429}
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