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

3 Answers
Mar 23, 2018

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)

Mar 23, 2018

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

Mar 24, 2018

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}