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Simplifying 4v2 + 32v + -156 = 0 Reorder the terms: -156 + 32v + 4v2 = 0 Solving -156 + 32v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-39 + 8v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-39 + 8v + v2)' equal to zero and attempt to solve: Simplifying -39 + 8v + v2 = 0 Solving -39 + 8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 8v + 39 + v2 = 0 + 39 Reorder the terms: -39 + 39 + 8v + v2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 8v + v2 = 0 + 39 8v + v2 = 0 + 39 Combine like terms: 0 + 39 = 39 8v + v2 = 39 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = 39 + 16 Reorder the terms: 16 + 8v + v2 = 39 + 16 Combine like terms: 39 + 16 = 55 16 + 8v + v2 = 55 Factor a perfect square on the left side: (v + 4)(v + 4) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (v + 4) equal to 7.416198487 and -7.416198487.Subproblem 1
v + 4 = 7.416198487 Simplifying v + 4 = 7.416198487 Reorder the terms: 4 + v = 7.416198487 Solving 4 + v = 7.416198487 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 7.416198487 + -4 Combine like terms: 4 + -4 = 0 0 + v = 7.416198487 + -4 v = 7.416198487 + -4 Combine like terms: 7.416198487 + -4 = 3.416198487 v = 3.416198487 Simplifying v = 3.416198487Subproblem 2
v + 4 = -7.416198487 Simplifying v + 4 = -7.416198487 Reorder the terms: 4 + v = -7.416198487 Solving 4 + v = -7.416198487 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -7.416198487 + -4 Combine like terms: 4 + -4 = 0 0 + v = -7.416198487 + -4 v = -7.416198487 + -4 Combine like terms: -7.416198487 + -4 = -11.416198487 v = -11.416198487 Simplifying v = -11.416198487Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.416198487, -11.416198487}Solution
v = {3.416198487, -11.416198487}
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