Extracting Square Roots: Applying the formula

We first rearrange and then set the equations to equal zero.

$x^2-49=0$

$x^2-7^2=0$

We use the abbreviated multiplication formula:

$(x-7)(x+7)=0$

$x=\pm7$

First, we move the terms to one side equal to 0.

$2x^2-x^2-8-4=0$

We simplify :

$x^2-12=0$

We use the shortcut multiplication formula to solve:

$x^2-(\sqrt{12})^2=0$

$(x-\sqrt{12})(x+\sqrt{12})=0$

$x=\pm\sqrt{12}$

Please note that the equation can be arranged differently:

x²-16 = x +4

x² - 4² = x +4

We will first factor a trinomial for the section on the left

(x-4)(x+4) = x+4

We will then divide everything by x+4

(x-4)(x+4) / x+4 = x+4 / x+4

x-4 = 1

x = 5