X^2+(a-b)x+ab=0

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Solution for X^2+(a-b)x+ab=0 equation:


Simplifying
X2 + (a + -1b) * x + ab = 0

Reorder the terms for easier multiplication:
X2 + x(a + -1b) + ab = 0
X2 + (a * x + -1b * x) + ab = 0
X2 + (ax + -1bx) + ab = 0

Reorder the terms:
X2 + ab + ax + -1bx = 0

Solving
X2 + ab + ax + -1bx = 0

Solving for variable 'X'.

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

Add '-1ab' to each side of the equation.
X2 + ab + ax + -1ab + -1bx = 0 + -1ab

Reorder the terms:
X2 + ab + -1ab + ax + -1bx = 0 + -1ab

Combine like terms: ab + -1ab = 0
X2 + 0 + ax + -1bx = 0 + -1ab
X2 + ax + -1bx = 0 + -1ab
Remove the zero:
X2 + ax + -1bx = -1ab

Add '-1ax' to each side of the equation.
X2 + ax + -1ax + -1bx = -1ab + -1ax

Combine like terms: ax + -1ax = 0
X2 + 0 + -1bx = -1ab + -1ax
X2 + -1bx = -1ab + -1ax

Add 'bx' to each side of the equation.
X2 + -1bx + bx = -1ab + -1ax + bx

Combine like terms: -1bx + bx = 0
X2 + 0 = -1ab + -1ax + bx
X2 = -1ab + -1ax + bx

Simplifying
X2 = -1ab + -1ax + bx

Reorder the terms:
X2 + ab + ax + -1bx = -1ab + ab + -1ax + ax + bx + -1bx

Combine like terms: -1ab + ab = 0
X2 + ab + ax + -1bx = 0 + -1ax + ax + bx + -1bx
X2 + ab + ax + -1bx = -1ax + ax + bx + -1bx

Combine like terms: -1ax + ax = 0
X2 + ab + ax + -1bx = 0 + bx + -1bx
X2 + ab + ax + -1bx = bx + -1bx

Combine like terms: bx + -1bx = 0
X2 + ab + ax + -1bx = 0

The solution to this equation could not be determined.

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