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}#