4m^4+4=17m^2

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Solution for 4m^4+4=17m^2 equation:


Simplifying
4m4 + 4 = 17m2

Reorder the terms:
4 + 4m4 = 17m2

Solving
4 + 4m4 = 17m2

Solving for variable 'm'.

Reorder the terms:
4 + -17m2 + 4m4 = 17m2 + -17m2

Combine like terms: 17m2 + -17m2 = 0
4 + -17m2 + 4m4 = 0

Factor a trinomial.
(1 + -4m2)(4 + -1m2) = 0

Factor a difference between two squares.
((1 + 2m)(1 + -2m))(4 + -1m2) = 0

Factor a difference between two squares.
((2 + m)(2 + -1m))(1 + 2m)(1 + -2m) = 0

Subproblem 1

Set the factor '(1 + 2m)' equal to zero and attempt to solve: Simplifying 1 + 2m = 0 Solving 1 + 2m = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2m = 0 + -1 2m = 0 + -1 Combine like terms: 0 + -1 = -1 2m = -1 Divide each side by '2'. m = -0.5 Simplifying m = -0.5

Subproblem 2

Set the factor '(1 + -2m)' equal to zero and attempt to solve: Simplifying 1 + -2m = 0 Solving 1 + -2m = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2m = 0 + -1 -2m = 0 + -1 Combine like terms: 0 + -1 = -1 -2m = -1 Divide each side by '-2'. m = 0.5 Simplifying m = 0.5

Subproblem 3

Set the factor '(2 + m)' equal to zero and attempt to solve: Simplifying 2 + m = 0 Solving 2 + m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + m = 0 + -2 m = 0 + -2 Combine like terms: 0 + -2 = -2 m = -2 Simplifying m = -2

Subproblem 4

Set the factor '(2 + -1m)' equal to zero and attempt to solve: Simplifying 2 + -1m = 0 Solving 2 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1m = 0 + -2 -1m = 0 + -2 Combine like terms: 0 + -2 = -2 -1m = -2 Divide each side by '-1'. m = 2 Simplifying m = 2

Solution

m = {-0.5, 0.5, -2, 2}

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