(x+a)(x+b)=x^2-100x+25

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Solution for (x+a)(x+b)=x^2-100x+25 equation: 


Simplifying
(x + a)(x + b) = x2 + -100x + 25

Reorder the terms:
(a + x)(x + b) = x2 + -100x + 25

Reorder the terms:
(a + x)(b + x) = x2 + -100x + 25

Multiply (a + x) * (b + x)
(a(b + x) + x(b + x)) = x2 + -100x + 25
((b * a + x * a) + x(b + x)) = x2 + -100x + 25
((ab + ax) + x(b + x)) = x2 + -100x + 25
(ab + ax + (b * x + x * x)) = x2 + -100x + 25
(ab + ax + (bx + x2)) = x2 + -100x + 25
(ab + ax + bx + x2) = x2 + -100x + 25

Reorder the terms:
ab + ax + bx + x2 = 25 + -100x + x2

Add '-1x2' to each side of the equation.
ab + ax + bx + x2 + -1x2 = 25 + -100x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx + 0 = 25 + -100x + x2 + -1x2
ab + ax + bx = 25 + -100x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx = 25 + -100x + 0
ab + ax + bx = 25 + -100x

Solving
ab + ax + bx = 25 + -100x

Solving for variable 'a'.

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

Add '-1bx' to each side of the equation.
ab + ax + bx + -1bx = 25 + -1bx + -100x

Combine like terms: bx + -1bx = 0
ab + ax + 0 = 25 + -1bx + -100x
ab + ax = 25 + -1bx + -100x

Reorder the terms:
-25 + ab + ax + bx + 100x = 25 + -1bx + -100x + -25 + bx + 100x

Reorder the terms:
-25 + ab + ax + bx + 100x = 25 + -25 + -1bx + bx + -100x + 100x

Combine like terms: 25 + -25 = 0
-25 + ab + ax + bx + 100x = 0 + -1bx + bx + -100x + 100x
-25 + ab + ax + bx + 100x = -1bx + bx + -100x + 100x

Combine like terms: -1bx + bx = 0
-25 + ab + ax + bx + 100x = 0 + -100x + 100x
-25 + ab + ax + bx + 100x = -100x + 100x

Combine like terms: -100x + 100x = 0
-25 + ab + ax + bx + 100x = 0

The solution to this equation could not be determined.

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