Question

Solve for $x$:

$\sqrt{2x+9}+x=13$

Answer 1

$\sqrt{2x+9}=13-x$

(Squaring both sides)

${\left(\sqrt{2x+9}\right)}^2={\left(13-x\right)}^2$

$2x+9=169+x^2-26x$

Rearrange the above equation,

$$\begin{gathered} x^2-26x-2x+169-9=0 \\ {x}^2-28x+160=0 \end{gathered}$$

Using factorization method,

$x^2-20x-8x+160=0$

$x(x-20)-8(x-20)=0$

$\left(x-20\right)\left(x-8\right)=0$

$$\begin{gathered} x-20=0orx-8=0 \\ x=20orx=8 \end{gathered}$$

However $x=20$ does not satisfy the given equation so $x=8$is the solution of the given equation.