v^4-49=0

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Solution for v^4-49=0 equation:


Simplifying
v4 + -49 = 0

Reorder the terms:
-49 + v4 = 0

Solving
-49 + v4 = 0

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '49' to each side of the equation.
-49 + 49 + v4 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + v4 = 0 + 49
v4 = 0 + 49

Combine like terms: 0 + 49 = 49
v4 = 49

Simplifying
v4 = 49

Reorder the terms:
-49 + v4 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + v4 = 0

Factor a difference between two squares.
(7 + v2)(-7 + v2) = 0

Subproblem 1

Set the factor '(7 + v2)' equal to zero and attempt to solve: Simplifying 7 + v2 = 0 Solving 7 + v2 = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v2 = 0 + -7 v2 = 0 + -7 Combine like terms: 0 + -7 = -7 v2 = -7 Simplifying v2 = -7 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-7 + v2)' equal to zero and attempt to solve: Simplifying -7 + v2 = 0 Solving -7 + v2 = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + v2 = 0 + 7 v2 = 0 + 7 Combine like terms: 0 + 7 = 7 v2 = 7 Simplifying v2 = 7 Take the square root of each side: v = {-2.645751311, 2.645751311}

Solution

v = {-2.645751311, 2.645751311}

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