How do you solve ( x + 1 )^2 =25?

May 8, 2016

Use the difference of squares identity to find:

$x = 4$ or $x = - 6$

Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Use this with $a = \left(x + 1\right)$ and $b = 5$ as follows...

Subtract $25$ from both sides of the equation to find:

$0 = {\left(x + 1\right)}^{2} - 25$

$= {\left(x + 1\right)}^{2} - {5}^{2}$

$= \left(\left(x + 1\right) - 5\right) \left(\left(x + 1\right) + 5\right)$

$= \left(x - 4\right) \left(x + 6\right)$

Hence $x = 4$ or $x = - 6$