40a^4-40a^2+10=

Solution for 40a^4-40a^2+10= equation:

Simplifying
40a4 + -40a2 + 10 = 0

Reorder the terms:
10 + -40a2 + 40a4 = 0

Solving
10 + -40a2 + 40a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -4a2 + 4a4) = 0

Factor a trinomial.
10((1 + -2a2)(1 + -2a2)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(1 + -2a2)' equal to zero and attempt to solve:

Simplifying
1 + -2a2 = 0

Solving
1 + -2a2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a2 = 0 + -1
-2a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2a2 = -1

Divide each side by '-2'.
a2 = 0.5

Simplifying
a2 = 0.5

Take the square root of each side:
a = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(1 + -2a2)' equal to zero and attempt to solve:

Simplifying
1 + -2a2 = 0

Solving
1 + -2a2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a2 = 0 + -1
-2a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2a2 = -1

Divide each side by '-2'.
a2 = 0.5

Simplifying
a2 = 0.5

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