(x+a)(x-b)=x^2-1

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Solution for (x+a)(x-b)=x^2-1 equation:


Simplifying
(x + a)(x + -1b) = x2 + -1

Reorder the terms:
(a + x)(x + -1b) = x2 + -1

Reorder the terms:
(a + x)(-1b + x) = x2 + -1

Multiply (a + x) * (-1b + x)
(a(-1b + x) + x(-1b + x)) = x2 + -1
((-1b * a + x * a) + x(-1b + x)) = x2 + -1
((-1ab + ax) + x(-1b + x)) = x2 + -1
(-1ab + ax + (-1b * x + x * x)) = x2 + -1
(-1ab + ax + (-1bx + x2)) = x2 + -1
(-1ab + ax + -1bx + x2) = x2 + -1

Reorder the terms:
-1ab + ax + -1bx + x2 = -1 + x2

Add '-1x2' to each side of the equation.
-1ab + ax + -1bx + x2 + -1x2 = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1ab + ax + -1bx + 0 = -1 + x2 + -1x2
-1ab + ax + -1bx = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1ab + ax + -1bx = -1 + 0
-1ab + ax + -1bx = -1

Solving
-1ab + ax + -1bx = -1

Solving for variable 'a'.

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

Add 'bx' to each side of the equation.
-1ab + ax + -1bx + bx = -1 + bx

Combine like terms: -1bx + bx = 0
-1ab + ax + 0 = -1 + bx
-1ab + ax = -1 + bx

Reorder the terms:
1 + -1ab + ax + -1bx = -1 + bx + 1 + -1bx

Reorder the terms:
1 + -1ab + ax + -1bx = -1 + 1 + bx + -1bx

Combine like terms: -1 + 1 = 0
1 + -1ab + ax + -1bx = 0 + bx + -1bx
1 + -1ab + ax + -1bx = bx + -1bx

Combine like terms: bx + -1bx = 0
1 + -1ab + ax + -1bx = 0

The solution to this equation could not be determined.

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