Question

If $\sqrt{10x+35}=x+6$ what is/ are the value(s) of $\frac{x}{2}$.

• A. $-\frac{1}{2}$
• B. $-\frac{7}{2}$
• C. $-\frac{1}{2}$ and $-\frac{7}{2}$
• D. $0$ and $-\frac{1}{2}$

Answer 1

The correct option is A $-\frac{1}{2}$

Given, $\sqrt{10x+35}=x+6$

Squaring both the sides, we get

$\Rightarrow 10x+35=(x+6{)}^2$

$\Rightarrow 10x+35=x^2+12x+36$

$\Rightarrow x^2+12x-10x+36-35=0$

$\Rightarrow x^2+2x+1=0$

$\Rightarrow x^2+x+x+1=0$

$\Rightarrow x(x+1)+1(x+1)=0$

$\Rightarrow (x+1)(x+1)=0$

$\Rightarrow x=-1$

$\therefore \frac{x}{2}=-\frac{1}{2}$