0=2x^4-15x^2+7

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Solution for 0=2x^4-15x^2+7 equation: 


Simplifying
0 = 2x4 + -15x2 + 7

Reorder the terms:
0 = 7 + -15x2 + 2x4

Solving
0 = 7 + -15x2 + 2x4

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + 15x2 + -2x4 = 7 + -15x2 + 2x4 + -7 + 15x2 + -2x4

Reorder the terms:
-7 + 15x2 + -2x4 = 7 + -7 + -15x2 + 15x2 + 2x4 + -2x4

Combine like terms: 7 + -7 = 0
-7 + 15x2 + -2x4 = 0 + -15x2 + 15x2 + 2x4 + -2x4
-7 + 15x2 + -2x4 = -15x2 + 15x2 + 2x4 + -2x4

Combine like terms: -15x2 + 15x2 = 0
-7 + 15x2 + -2x4 = 0 + 2x4 + -2x4
-7 + 15x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
-7 + 15x2 + -2x4 = 0

Factor a trinomial.
(-7 + x2)(1 + -2x2) = 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 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 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 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {-2.645751311, 2.645751311, -0.707106781, 0.707106781}

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