0=4x^4-29x^2+7

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Solution for 0=4x^4-29x^2+7 equation: 


Simplifying
0 = 4x4 + -29x2 + 7

Reorder the terms:
0 = 7 + -29x2 + 4x4

Solving
0 = 7 + -29x2 + 4x4

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + 29x2 + -4x4 = 7 + -29x2 + 4x4 + -7 + 29x2 + -4x4

Reorder the terms:
-7 + 29x2 + -4x4 = 7 + -7 + -29x2 + 29x2 + 4x4 + -4x4

Combine like terms: 7 + -7 = 0
-7 + 29x2 + -4x4 = 0 + -29x2 + 29x2 + 4x4 + -4x4
-7 + 29x2 + -4x4 = -29x2 + 29x2 + 4x4 + -4x4

Combine like terms: -29x2 + 29x2 = 0
-7 + 29x2 + -4x4 = 0 + 4x4 + -4x4
-7 + 29x2 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-7 + 29x2 + -4x4 = 0

Factor a trinomial.
(-7 + x2)(1 + -4x2) = 0

Factor a difference between two squares.
(-7 + x2)((1 + 2x)(1 + -2x)) = 0


Subproblem 1
Set the factor '(-7 + x2)' equal to zero and attempt to solve:

Simplifying
-7 + x2 = 0

Solving
-7 + x2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x2 = 0 + 7
x2 = 0 + 7

Combine like terms: 0 + 7 = 7
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-2.645751311, 2.645751311, -0.5, 0.5}

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