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Simplifying (v2 + -6) * v2 + 4 = 0 Reorder the terms: (-6 + v2) * v2 + 4 = 0 Reorder the terms for easier multiplication: v2(-6 + v2) + 4 = 0 (-6 * v2 + v2 * v2) + 4 = 0 (-6v2 + v4) + 4 = 0 Reorder the terms: 4 + -6v2 + v4 = 0 Solving 4 + -6v2 + 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 + -6v2 + -4 + v4 = 0 + -4 Reorder the terms: 4 + -4 + -6v2 + v4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6v2 + v4 = 0 + -4 -6v2 + v4 = 0 + -4 Combine like terms: 0 + -4 = -4 -6v2 + v4 = -4 The v term is -6v2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v2 + 9 + v4 = -4 + 9 Reorder the terms: 9 + -6v2 + v4 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6v2 + v4 = 5 Factor a perfect square on the left side: (v2 + -3)(v2 + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (v2 + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
v2 + -3 = 2.236067978 Simplifying v2 + -3 = 2.236067978 Reorder the terms: -3 + v2 = 2.236067978 Solving -3 + v2 = 2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v2 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + v2 = 2.236067978 + 3 v2 = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 v2 = 5.236067978 Simplifying v2 = 5.236067978 Take the square root of each side: v = {-2.288245611, 2.288245611}Subproblem 2
v2 + -3 = -2.236067978 Simplifying v2 + -3 = -2.236067978 Reorder the terms: -3 + v2 = -2.236067978 Solving -3 + v2 = -2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v2 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + v2 = -2.236067978 + 3 v2 = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 v2 = 0.763932022 Simplifying v2 = 0.763932022 Take the square root of each side: v = {-0.874032049, 0.874032049}Solution
The solution to the problem is based on the solutions from the subproblems. v = {-2.288245611, 2.288245611, -0.874032049, 0.874032049}
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