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Simplifying 10v2 + 4v + -22 = 0 Reorder the terms: -22 + 4v + 10v2 = 0 Solving -22 + 4v + 10v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 2v + 5v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 2v + 5v2)' equal to zero and attempt to solve: Simplifying -11 + 2v + 5v2 = 0 Solving -11 + 2v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 0.4v + v2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.4v + 2.2 + v2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.4v + v2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.4v + v2 = 0 + 2.2 0.4v + v2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.4v + v2 = 2.2 The v term is 0.4v. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4v + 0.04 + v2 = 2.2 + 0.04 Reorder the terms: 0.04 + 0.4v + v2 = 2.2 + 0.04 Combine like terms: 2.2 + 0.04 = 2.24 0.04 + 0.4v + v2 = 2.24 Factor a perfect square on the left side: (v + 0.2)(v + 0.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (v + 0.2) equal to 1.496662955 and -1.496662955.Subproblem 1
v + 0.2 = 1.496662955 Simplifying v + 0.2 = 1.496662955 Reorder the terms: 0.2 + v = 1.496662955 Solving 0.2 + v = 1.496662955 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + v = 1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + v = 1.496662955 + -0.2 v = 1.496662955 + -0.2 Combine like terms: 1.496662955 + -0.2 = 1.296662955 v = 1.296662955 Simplifying v = 1.296662955Subproblem 2
v + 0.2 = -1.496662955 Simplifying v + 0.2 = -1.496662955 Reorder the terms: 0.2 + v = -1.496662955 Solving 0.2 + v = -1.496662955 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + v = -1.496662955 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + v = -1.496662955 + -0.2 v = -1.496662955 + -0.2 Combine like terms: -1.496662955 + -0.2 = -1.696662955 v = -1.696662955 Simplifying v = -1.696662955Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.296662955, -1.696662955}Solution
v = {1.296662955, -1.696662955}
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