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Simplifying 4v2 + 4v + -116 = 0 Reorder the terms: -116 + 4v + 4v2 = 0 Solving -116 + 4v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-29 + v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-29 + v + v2)' equal to zero and attempt to solve: Simplifying -29 + v + v2 = 0 Solving -29 + v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + v + 29 + v2 = 0 + 29 Reorder the terms: -29 + 29 + v + v2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + v + v2 = 0 + 29 v + v2 = 0 + 29 Combine like terms: 0 + 29 = 29 v + v2 = 29 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. v + 0.25 + v2 = 29 + 0.25 Reorder the terms: 0.25 + v + v2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 0.25 + v + v2 = 29.25 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (v + 0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
v + 0.5 = 5.408326913 Simplifying v + 0.5 = 5.408326913 Reorder the terms: 0.5 + v = 5.408326913 Solving 0.5 + v = 5.408326913 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 5.408326913 + -0.5 v = 5.408326913 + -0.5 Combine like terms: 5.408326913 + -0.5 = 4.908326913 v = 4.908326913 Simplifying v = 4.908326913Subproblem 2
v + 0.5 = -5.408326913 Simplifying v + 0.5 = -5.408326913 Reorder the terms: 0.5 + v = -5.408326913 Solving 0.5 + v = -5.408326913 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -5.408326913 + -0.5 v = -5.408326913 + -0.5 Combine like terms: -5.408326913 + -0.5 = -5.908326913 v = -5.908326913 Simplifying v = -5.908326913Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.908326913, -5.908326913}Solution
v = {4.908326913, -5.908326913}
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