a*a-b*b=(x-1)*(x-1)

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Solution for a*a-b*b=(x-1)*(x-1) equation: 


Simplifying
a * a + -1b * b = (x + -1)(x + -1)

Multiply a * a
a2 + -1b * b = (x + -1)(x + -1)

Multiply b * b
a2 + -1b2 = (x + -1)(x + -1)

Reorder the terms:
a2 + -1b2 = (-1 + x)(x + -1)

Reorder the terms:
a2 + -1b2 = (-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
a2 + -1b2 = (-1(-1 + x) + x(-1 + x))
a2 + -1b2 = ((-1 * -1 + x * -1) + x(-1 + x))
a2 + -1b2 = ((1 + -1x) + x(-1 + x))
a2 + -1b2 = (1 + -1x + (-1 * x + x * x))
a2 + -1b2 = (1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
a2 + -1b2 = (1 + -2x + x2)

Solving
a2 + -1b2 = 1 + -2x + x2

Solving for variable 'a'.

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

Add 'b2' to each side of the equation.
a2 + -1b2 + b2 = 1 + -2x + b2 + x2

Combine like terms: -1b2 + b2 = 0
a2 + 0 = 1 + -2x + b2 + x2
a2 = 1 + -2x + b2 + x2

Reorder the terms:
a2 = 1 + b2 + -2x + x2

Simplifying
a2 = 1 + b2 + -2x + x2

Reorder the terms:
-1 + a2 + -1b2 + 2x + -1x2 = 1 + b2 + -2x + x2 + -1 + -1b2 + 2x + -1x2

Reorder the terms:
-1 + a2 + -1b2 + 2x + -1x2 = 1 + -1 + b2 + -1b2 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-1 + a2 + -1b2 + 2x + -1x2 = 0 + b2 + -1b2 + -2x + 2x + x2 + -1x2
-1 + a2 + -1b2 + 2x + -1x2 = b2 + -1b2 + -2x + 2x + x2 + -1x2

Combine like terms: b2 + -1b2 = 0
-1 + a2 + -1b2 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-1 + a2 + -1b2 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-1 + a2 + -1b2 + 2x + -1x2 = 0 + x2 + -1x2
-1 + a2 + -1b2 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + a2 + -1b2 + 2x + -1x2 = 0

The solution to this equation could not be determined.

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