# How do you solve x^2 - 49 = 0 ?

Mar 17, 2016

${x}_{1 , 2} = \pm 7$

#### Explanation:

You could use several methods.

The fastest is:

${x}^{2} = 49$

$\therefore \sqrt{{x}^{2}} = \pm \sqrt{49}$

${x}_{1 , 2} = \pm 7$

I'd prefer to factorize the equation using the Square Difference Identitiy:

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

to rewrite the second degree equation as product of first degree equation.

$\left({x}^{2} - 49\right) = 0 \iff \left({x}^{2} - {7}^{2}\right) = 0 \iff \left(x + 7\right) \left(x - 7\right) = 0$
$\therefore \left(x + 7\right) = 0 \implies {x}_{1} = - 7$
$\therefore \left(x - 7\right) = 0 \implies {x}_{2} = 7$
${x}_{1 , 2} = \pm 7$