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Simplifying v2 + 4v + -3 = 0 Reorder the terms: -3 + 4v + v2 = 0 Solving -3 + 4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + 4v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4v + v2 = 0 + 3 4v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 4v + v2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4v + v2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4v + v2 = 7 Factor a perfect square on the left side: (v + 2)(v + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (v + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
v + 2 = 2.645751311 Simplifying v + 2 = 2.645751311 Reorder the terms: 2 + v = 2.645751311 Solving 2 + v = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + v = 2.645751311 + -2 v = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 v = 0.645751311 Simplifying v = 0.645751311Subproblem 2
v + 2 = -2.645751311 Simplifying v + 2 = -2.645751311 Reorder the terms: 2 + v = -2.645751311 Solving 2 + v = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + v = -2.645751311 + -2 v = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 v = -4.645751311 Simplifying v = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.645751311, -4.645751311}
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