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Simplifying 10v2 + 20v + -2 = 8 Reorder the terms: -2 + 20v + 10v2 = 8 Solving -2 + 20v + 10v2 = 8 Solving for variable 'v'. Reorder the terms: -2 + -8 + 20v + 10v2 = 8 + -8 Combine like terms: -2 + -8 = -10 -10 + 20v + 10v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -10 + 20v + 10v2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-1 + 2v + v2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1 + 2v + v2)' equal to zero and attempt to solve: Simplifying -1 + 2v + v2 = 0 Solving -1 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 2v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2v + v2 = 0 + 1 2v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 2v + v2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2v + v2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2v + v2 = 2 Factor a perfect square on the left side: (v + 1)(v + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (v + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
v + 1 = 1.414213562 Simplifying v + 1 = 1.414213562 Reorder the terms: 1 + v = 1.414213562 Solving 1 + v = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + v = 1.414213562 + -1 v = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 v = 0.414213562 Simplifying v = 0.414213562Subproblem 2
v + 1 = -1.414213562 Simplifying v + 1 = -1.414213562 Reorder the terms: 1 + v = -1.414213562 Solving 1 + v = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + v = -1.414213562 + -1 v = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 v = -2.414213562 Simplifying v = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.414213562, -2.414213562}Solution
v = {0.414213562, -2.414213562}
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