What is the answer to (x+a)(x-b)=x^2+2x-48 ?

The answer to (x+a)(x-b)=x^2+2x-48 is x=(-48+ab)/(a-b-2);\quad a\ne b+2

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(x+a)(x-b)=x^2+2x-48

(x + a) (x - b) = x^{2} + 2 x - 48

x = \frac{- 48 + ab}{a - b - 2}; a \neq = b + 2

Solution steps

(x + a) (x - b) = x^{2} + 2 x - 48

Expand

(x + a) (x - b) : x^{2} - b x + a x - ab

x^{2} - b x + a x - ab = x^{2} + 2 x - 48

Move

ab

to the right side

x^{2} - b x + a x = x^{2} + 2 x - 48 + ab

Subtract

x^{2} + 2 x

from both sides

x^{2} - b x + a x - (x^{2} + 2 x) = x^{2} + 2 x - 48 + ab - (x^{2} + 2 x)

Simplify

a x - b x - 2 x = - 48 + ab

Factor

a x - b x - 2 x : x (a - b - 2)

x (a - b - 2) = - 48 + ab

Divide both sides by

a - b - 2; a \neq = b + 2

x = \frac{- 48 + ab}{a - b - 2}; a \neq = b + 2

- 4 x - 8 = 52

x = \frac{1}{2} x

4 x + 5 + x = 2 + 3 x + 3

\frac{x}{2} - \frac{2}{3} = \frac{x}{4} - 1

20 x + 5 = 24 x - 1

What is the answer to (x+a)(x-b)=x^2+2x-48 ?
The answer to (x+a)(x-b)=x^2+2x-48 is x=(-48+ab)/(a-b-2);\quad a\ne b+2