# How do you solve x^2-14x-49=0?

Mar 23, 2018

$x = 7 \pm 7 \sqrt{2}$

#### Explanation:

${x}^{2} - 14 x - 49 = 0$

This is unfactorable, therefore you would use the quadratic formula,

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 1$

$b = - 14$

$c = - 49$

Plug in the values a, b and c accordingly.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- \left(- 14\right) \pm \sqrt{{\left(- 14\right)}^{2} - 4 \left(1\right) \left(- 49\right)}}{2 \left(1\right)}$

$= \frac{14 \pm \sqrt{196 + 196}}{2}$

$= \frac{14 \pm \sqrt{392}}{2}$

$= \frac{14 \pm 14 \sqrt{2}}{2}$

$x = 7 \pm 7 \sqrt{2}$

Mar 23, 2018

$x = 7 + 7 \sqrt{2} \mathmr{and} x = 7 - 7 \sqrt{2}$

#### Explanation:

${x}^{2} - 14 x - 49 = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Where $a = 1 , b = - 14 , c = - 49$

=(-(-14)+-sqrt((-14)^2-4(1)(-49)))/((2)(1)

$x = \frac{14 \pm \sqrt{196 + 196}}{2}$

$x = \frac{14 \pm \sqrt{392}}{2}$

$x = 7 + 7 \sqrt{2} \mathmr{and} x = 7 - 7 \sqrt{2}$

Mar 24, 2018

Using the quadratic formula, you find that $x = \left\{16.8995 , - 2.8995\right\}$

#### Explanation:

The quadratic formula uses a quadratic equation. The equation looks like this:

$a {x}^{2} + b x + c$

...and the formula looks like this:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

For this setup:
$a = 1$
$b = - 14$
$c = - 49$

Plugging that into the formula:

$x = \frac{- \left(- 14\right) \pm \sqrt{{\left(- 14\right)}^{2} - 4 \left(1\right) \left(- 49\right)}}{2 \left(1\right)}$

$x = \frac{14 \pm \sqrt{196 + 196}}{2}$

$x = \frac{14 \pm \sqrt{2 \times 196}}{2} \Rightarrow x = \frac{14 \pm 14 \sqrt{2}}{2}$

x=7+-7sqrt(2)rArr color(red)(x={16.8995,-2.8995}