Question

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

Answer 1

`x=7+-7sqrt(2)`

Explanation:

`x^2-14x-49=0`

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

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`a=1`

`b=-14`

`c=-49`

Plug in the values a, b and c accordingly.

`x=(-b+-sqrt(b^2-4ac))/(2a)`

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

`=(14+-sqrt(196+196))/(2)`

`=(14+-sqrt(392))/(2)`

`=(14+-14sqrt(2))/(2)`

`x=7+-7sqrt(2)`

Answer 2

`x=7+7sqrt2 or x=7-7sqrt2`

Explanation:

`x^2-14x - 49 =0`

Use the quadratic formula

`x=(-b+-sqrt(b^2-4ac))/(2a)`

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

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

`x=(14+-sqrt(196+196))/(2)`

`x=(14+-sqrt392)/2`

`x= 7 + 7sqrt2 or x=7 - 7sqrt2`

Answer 3

Using the quadratic formula, you find that `x={16.8995,-2.8995}`

Explanation:

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

`ax^2+bx+c`

...and the formula looks like this:

`x=(-b+-sqrt(b^2-4ac))/(2a)`

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

Plugging that into the formula:

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

`x=(14+-sqrt(196+196))/(2)`

`x=(14+-sqrt(2xx196))/(2) rArr x=(14+-14sqrt(2))/(2)`

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