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Simplifying 2v2 + 8v + -12 = 0 Reorder the terms: -12 + 8v + 2v2 = 0 Solving -12 + 8v + 2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 4v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 4v + v2)' equal to zero and attempt to solve: Simplifying -6 + 4v + v2 = 0 Solving -6 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + 4v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4v + v2 = 0 + 6 4v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 4v + v2 = 6 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 6 + 4 Reorder the terms: 4 + 4v + v2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4v + v2 = 10 Factor a perfect square on the left side: (v + 2)(v + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (v + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
v + 2 = 3.16227766 Simplifying v + 2 = 3.16227766 Reorder the terms: 2 + v = 3.16227766 Solving 2 + v = 3.16227766 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + v = 3.16227766 + -2 v = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 v = 1.16227766 Simplifying v = 1.16227766Subproblem 2
v + 2 = -3.16227766 Simplifying v + 2 = -3.16227766 Reorder the terms: 2 + v = -3.16227766 Solving 2 + v = -3.16227766 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + v = -3.16227766 + -2 v = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 v = -5.16227766 Simplifying v = -5.16227766Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.16227766, -5.16227766}Solution
v = {1.16227766, -5.16227766}
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