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Simplifying v4 + -8v2 + 4 = 0 Reorder the terms: 4 + -8v2 + v4 = 0 Solving 4 + -8v2 + v4 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8v2 + -4 + v4 = 0 + -4 Reorder the terms: 4 + -4 + -8v2 + v4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8v2 + v4 = 0 + -4 -8v2 + v4 = 0 + -4 Combine like terms: 0 + -4 = -4 -8v2 + v4 = -4 The v term is -8v2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8v2 + 16 + v4 = -4 + 16 Reorder the terms: 16 + -8v2 + v4 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8v2 + v4 = 12 Factor a perfect square on the left side: (v2 + -4)(v2 + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (v2 + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
v2 + -4 = 3.464101615 Simplifying v2 + -4 = 3.464101615 Reorder the terms: -4 + v2 = 3.464101615 Solving -4 + v2 = 3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v2 = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + v2 = 3.464101615 + 4 v2 = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 v2 = 7.464101615 Simplifying v2 = 7.464101615 Take the square root of each side: v = {-2.732050808, 2.732050808}Subproblem 2
v2 + -4 = -3.464101615 Simplifying v2 + -4 = -3.464101615 Reorder the terms: -4 + v2 = -3.464101615 Solving -4 + v2 = -3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v2 = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + v2 = -3.464101615 + 4 v2 = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 v2 = 0.535898385 Simplifying v2 = 0.535898385 Take the square root of each side: v = {-0.732050808, 0.732050808}Solution
The solution to the problem is based on the solutions from the subproblems. v = {-2.732050808, 2.732050808, -0.732050808, 0.732050808}
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