# How do you solve x^2-7x=5 using the quadratic formula?

Aug 8, 2015

$x = \frac{7 + \sqrt{69}}{2}$
or
$x = \frac{7 - \sqrt{69}}{2}$

#### Explanation:

Given ${x}^{2} - 7 x = 5$

Re-writing in standard form:
$\textcolor{w h i t e}{\text{XXXX}}$$1 {x}^{2} - 7 x - 5 = 0$

The general standard form for a quadratic is
$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x + c = 0$

The quadratic formula tells us that the solution for an equation in the general form is:
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Base on the re-written form of the given equation:
$a = 1$$\textcolor{w h i t e}{\text{XXXX}}$$b = - 7$$\textcolor{w h i t e}{\text{XXXX}}$$c = - 5$

So the solution is
$\textcolor{w h i t e}{\text{XXXX}}$x = (7+-sqrt((-7)^2-4(1)(-5)))/(2(1)

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{7 \pm \sqrt{69}}{2}$