Question

Solve for $x$
$\sqrt{2x+a}+x=13$

Answer 1

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

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

by squaring both sides

$2x+a=(13-x{)}^2$

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

$x^2-26x-2x+(169-a)=0$

$x^2-28x+(169-a)=0$

We have a formula for solving quadratic equation $a{x}^2+bx+c=0$ is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{28\pm \sqrt{{28}^2-4\left(1\right)(169-a)}}{2}$

$x=\frac{28\pm \sqrt{{28}^2-4(169-a)}}{2}$

$x=\frac{28\pm \sqrt{(4\times 7{)}^2-4(169-a)}}{2}$

$x=14\pm \sqrt{4\times 49-169+a}$

$x=14\pm \sqrt{27+a}$