1-a^2=x^2-2ax+1

Solution for 1-a^2=x^2-2ax+1 equation:

Simplifying
1 + -1a2 = x2 + -2ax + 1

Reorder the terms:
1 + -1a2 = 1 + -2ax + x2

Add '-1' to each side of the equation.
1 + -1 + -1a2 = 1 + -2ax + -1 + x2

Combine like terms: 1 + -1 = 0
0 + -1a2 = 1 + -2ax + -1 + x2
-1a2 = 1 + -2ax + -1 + x2

Reorder the terms:
-1a2 = 1 + -1 + -2ax + x2

Combine like terms: 1 + -1 = 0
-1a2 = 0 + -2ax + x2
-1a2 = -2ax + x2

Solving
-1a2 = -2ax + x2

Solving for variable 'a'.

Reorder the terms:
2ax + -1a2 + -1x2 = -2ax + x2 + 2ax + -1x2

Reorder the terms:
2ax + -1a2 + -1x2 = -2ax + 2ax + x2 + -1x2

Combine like terms: -2ax + 2ax = 0
2ax + -1a2 + -1x2 = 0 + x2 + -1x2
2ax + -1a2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2ax + -1a2 + -1x2 = 0

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

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

Simplifying
-1a + x = 0

Solving
-1a + x = 0

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

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

Combine like terms: x + -1x = 0
-1a + 0 = 0 + -1x
-1a = 0 + -1x
Remove the zero:
-1a = -1x

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

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

Combine like terms: -1x + x = 0
a + 0 = 0 + x
a = 0 + x
Remove the zero:
a = x

Simplifying
a = x
Solution
a = {x, x}