Question

Solve the equation and check the proposed solution. 2x X+5 - 2 = X-26 X-5 Select the correct choice below and, if necessary, fill in the answer box to complete your chol O A. X= (Simplify your answer. Use a comma to separate answers as needed.) OB. There is no solution. Click to select and enter your answer(s).

Answer 1

Answer:

x = -9 and 20

Explantion:

$\small \frac{2x}{x+5}-2=\frac{x-26}{x-5}$

$\small \Rightarrow \frac{2x-2(x+5)}{x+5}=\frac{x-26}{x-5}$

2Ꮖ - 2 - 10 . = Ꭲ +5 - 2Ꮾ Ꮧ - 5

-10 = - 2Ꮾ T - 5 2 +5

$\small \Rightarrow -10(x-5)=(x-26)(x+5)$

$\small \Rightarrow -10x+50=x^{2}-21x-130$

$\small \Rightarrow x^{2}-11x-180=0$

$\small x = \frac{-(-11)\pm \sqrt{(-11)^{2}-4\times 1\times (-180)}}{2\times 1}$

$\small x = \frac{11\pm \sqrt{841}}{2}$

$\small x = \frac{11\pm 29}{2}$

$\small x = -9, 20$