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Simplifying 2(v2 + 2v + -524) = 0 Reorder the terms: 2(-524 + 2v + v2) = 0 (-524 * 2 + 2v * 2 + v2 * 2) = 0 (-1048 + 4v + 2v2) = 0 Solving -1048 + 4v + 2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-524 + 2v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-524 + 2v + v2)' equal to zero and attempt to solve: Simplifying -524 + 2v + v2 = 0 Solving -524 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '524' to each side of the equation. -524 + 2v + 524 + v2 = 0 + 524 Reorder the terms: -524 + 524 + 2v + v2 = 0 + 524 Combine like terms: -524 + 524 = 0 0 + 2v + v2 = 0 + 524 2v + v2 = 0 + 524 Combine like terms: 0 + 524 = 524 2v + v2 = 524 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 524 + 1 Reorder the terms: 1 + 2v + v2 = 524 + 1 Combine like terms: 524 + 1 = 525 1 + 2v + v2 = 525 Factor a perfect square on the left side: (v + 1)(v + 1) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (v + 1) equal to 22.912878475 and -22.912878475.Subproblem 1
v + 1 = 22.912878475 Simplifying v + 1 = 22.912878475 Reorder the terms: 1 + v = 22.912878475 Solving 1 + v = 22.912878475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 22.912878475 + -1 Combine like terms: 1 + -1 = 0 0 + v = 22.912878475 + -1 v = 22.912878475 + -1 Combine like terms: 22.912878475 + -1 = 21.912878475 v = 21.912878475 Simplifying v = 21.912878475Subproblem 2
v + 1 = -22.912878475 Simplifying v + 1 = -22.912878475 Reorder the terms: 1 + v = -22.912878475 Solving 1 + v = -22.912878475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -22.912878475 + -1 Combine like terms: 1 + -1 = 0 0 + v = -22.912878475 + -1 v = -22.912878475 + -1 Combine like terms: -22.912878475 + -1 = -23.912878475 v = -23.912878475 Simplifying v = -23.912878475Solution
The solution to the problem is based on the solutions from the subproblems. v = {21.912878475, -23.912878475}Solution
v = {21.912878475, -23.912878475}
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