# How do you solve sqrt(4p+1)=2p-1?

May 7, 2016

$p = 0 \mathmr{and} p = 2$

#### Explanation:

First, square both sides of the equation.

${\left(\sqrt{4 p + 1}\right)}^{2} = {\left(2 p - 1\right)}^{2}$

$4 p + 1 = 4 {p}^{2} - 4 p + 1$

Move all terms to the same side so that one side of the equation is $0$.

$0 = 4 {p}^{2} - 4 p - 4 p + 1 - 1$

Combine like terms.

$0 = 4 {p}^{2} - 8 p$

Factorise a $4 p$
$0 = 4 p \left(p - 2\right)$

$4 p = 0 \mathmr{and} p - 2 = 0$

$p = 0 \mathmr{and} p = 2$