Question

solve for all values of x by factoring.
$x^2 + 4x - 14 = 4x$

Explanation:

Step1: Simplify the equation

Subtract $4x$ from both sides:
$x^2 + 4x - 14 - 4x = 4x - 4x$
$\implies x^2 - 14 = 0$

Step2: Rewrite as difference of squares

Express in factored form using $a^2 - b^2=(a-b)(a+b)$:
$x^2 - (\sqrt{14})^2 = 0$
$\implies (x - \sqrt{14})(x + \sqrt{14}) = 0$

Step3: Solve for x

Set each factor equal to 0:
$x - \sqrt{14} = 0 \implies x = \sqrt{14}$
$x + \sqrt{14} = 0 \implies x = -\sqrt{14}$

Answer:

$x = \sqrt{14}$ and $x = -\sqrt{14}$