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Simplifying v4 + -7v2 + 12 = 0 Reorder the terms: 12 + -7v2 + v4 = 0 Solving 12 + -7v2 + v4 = 0 Solving for variable 'v'. Factor a trinomial. (3 + -1v2)(4 + -1v2) = 0 Factor a difference between two squares. (3 + -1v2)((2 + v)(2 + -1v)) = 0Subproblem 1
Set the factor '(3 + -1v2)' equal to zero and attempt to solve: Simplifying 3 + -1v2 = 0 Solving 3 + -1v2 = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v2 = 0 + -3 -1v2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1v2 = -3 Divide each side by '-1'. v2 = 3 Simplifying v2 = 3 Take the square root of each side: v = {-1.732050808, 1.732050808}Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 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 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Subproblem 3
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Solution
v = {-1.732050808, 1.732050808, -2, 2}
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