Question

Solve for $x;\sqrt{6x+7}-(2x-7)=0$

Answer 1

Given equation $\sqrt{6x+7}-(2x-7)=0$
$\sqrt{6x+7}=(2x-7)$
Squaring on both sides, we get
$\Rightarrow (\sqrt{6x+7}{)}^2=(2x-7{)}^2$
$\Rightarrow 6x+7=(2x{)}^2+(7{)}^2-2\left(2x\right)\left(7\right)$ [Since, $(a-b{)}^2=a^2-2ab+b^2$]
$\Rightarrow 6x+7=4x^2+49-28x$
$\Rightarrow 4x^2-28x-6x+49-7=0$
$\Rightarrow 4x^2-34x+42=0$
$\Rightarrow 2x^2-17x+21=0$
$\Rightarrow 2x^2-14x-3x+21=0$
$\Rightarrow 2x(x-7)-3(x-7)=0$
$\Rightarrow (x-7)(2x-3)=0$
$\Rightarrow x-7=0$ or $2x-3=0$
$\therefore x=7$ or $x=\frac{3}{2}$