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Simplifying 4v2 + 20v + -160 = 0 Reorder the terms: -160 + 20v + 4v2 = 0 Solving -160 + 20v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 5v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-40 + 5v + v2)' equal to zero and attempt to solve: Simplifying -40 + 5v + v2 = 0 Solving -40 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 5v + 40 + v2 = 0 + 40 Reorder the terms: -40 + 40 + 5v + v2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 5v + v2 = 0 + 40 5v + v2 = 0 + 40 Combine like terms: 0 + 40 = 40 5v + v2 = 40 The v term is 5v. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5v + 6.25 + v2 = 40 + 6.25 Reorder the terms: 6.25 + 5v + v2 = 40 + 6.25 Combine like terms: 40 + 6.25 = 46.25 6.25 + 5v + v2 = 46.25 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (v + 2.5) equal to 6.800735254 and -6.800735254.Subproblem 1
v + 2.5 = 6.800735254 Simplifying v + 2.5 = 6.800735254 Reorder the terms: 2.5 + v = 6.800735254 Solving 2.5 + v = 6.800735254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = 6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 6.800735254 + -2.5 v = 6.800735254 + -2.5 Combine like terms: 6.800735254 + -2.5 = 4.300735254 v = 4.300735254 Simplifying v = 4.300735254Subproblem 2
v + 2.5 = -6.800735254 Simplifying v + 2.5 = -6.800735254 Reorder the terms: 2.5 + v = -6.800735254 Solving 2.5 + v = -6.800735254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = -6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -6.800735254 + -2.5 v = -6.800735254 + -2.5 Combine like terms: -6.800735254 + -2.5 = -9.300735254 v = -9.300735254 Simplifying v = -9.300735254Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.300735254, -9.300735254}Solution
v = {4.300735254, -9.300735254}
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