2a^2=1+a

Solution for 2a^2=1+a equation:

Simplifying
2a2 = 1 + a

Solving
2a2 = 1 + a

Solving for variable 'a'.

Reorder the terms:
-1 + -1a + 2a2 = 1 + a + -1 + -1a

Reorder the terms:
-1 + -1a + 2a2 = 1 + -1 + a + -1a

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

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

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

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

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

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

Simplifying
a = -0.5
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-0.5, 1}