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Simplifying (v + 2)(v + 2) + -50 = 0 Reorder the terms: (2 + v)(v + 2) + -50 = 0 Reorder the terms: (2 + v)(2 + v) + -50 = 0 Multiply (2 + v) * (2 + v) (2(2 + v) + v(2 + v)) + -50 = 0 ((2 * 2 + v * 2) + v(2 + v)) + -50 = 0 ((4 + 2v) + v(2 + v)) + -50 = 0 (4 + 2v + (2 * v + v * v)) + -50 = 0 (4 + 2v + (2v + v2)) + -50 = 0 Combine like terms: 2v + 2v = 4v (4 + 4v + v2) + -50 = 0 Reorder the terms: 4 + -50 + 4v + v2 = 0 Combine like terms: 4 + -50 = -46 -46 + 4v + v2 = 0 Solving -46 + 4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 4v + 46 + v2 = 0 + 46 Reorder the terms: -46 + 46 + 4v + v2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 4v + v2 = 0 + 46 4v + v2 = 0 + 46 Combine like terms: 0 + 46 = 46 4v + v2 = 46 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 46 + 4 Reorder the terms: 4 + 4v + v2 = 46 + 4 Combine like terms: 46 + 4 = 50 4 + 4v + v2 = 50 Factor a perfect square on the left side: (v + 2)(v + 2) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (v + 2) equal to 7.071067812 and -7.071067812.Subproblem 1
v + 2 = 7.071067812 Simplifying v + 2 = 7.071067812 Reorder the terms: 2 + v = 7.071067812 Solving 2 + v = 7.071067812 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 7.071067812 + -2 Combine like terms: 2 + -2 = 0 0 + v = 7.071067812 + -2 v = 7.071067812 + -2 Combine like terms: 7.071067812 + -2 = 5.071067812 v = 5.071067812 Simplifying v = 5.071067812Subproblem 2
v + 2 = -7.071067812 Simplifying v + 2 = -7.071067812 Reorder the terms: 2 + v = -7.071067812 Solving 2 + v = -7.071067812 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -7.071067812 + -2 Combine like terms: 2 + -2 = 0 0 + v = -7.071067812 + -2 v = -7.071067812 + -2 Combine like terms: -7.071067812 + -2 = -9.071067812 v = -9.071067812 Simplifying v = -9.071067812Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.071067812, -9.071067812}
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