How do you solve x^2 - 8x - 20 = 0 by completing the square?

2 Answers
May 14, 2016

x=10 or x=-2

Explanation:

In addition to completing the square we can use the difference of squares identity:

a^2-b^2 = (a-b)(a+b)

with a=(x-4) and b=6 as follows:

0 = x^2-8x-20

=(x-4)^2-4^2-20

=(x-4)^2-16-20

=(x-4)^2-36

=(x-4)^2-6^2

=((x-4)-6)((x-4)+6)

=(x-10)(x+2)

So x=10 or x=-2

May 14, 2016

x=10, -2

Explanation:

color(red)("We know that " (a+b)^2=a^2 +2ab+b^2

color(red)("And "(a-b)^2=a^2 -2ab+b^2

x^2-8x-20=0

This can be written as x^2+(2xx x xx-4)-20=0

Let a=x and b=-4

color(red)("Now, " (x-4)^2=x^2 -8x+16

x^2-8x-20=0

x^2-8x=20

Add 16 to both sides:

x^2-8xcolor(red)(+16)=20color(red)(+16)

(x-4)^2=36

We know that 36=6^2 " and " 36=-6^2

Find the square root of both the sides:

x-4=+-6

When, x-4=6

Add 4 to both sides:

x-4color(red)(+4)=6color(red)(+4)

x=10

When, x-4=-6

Add 4 to both sides:

x-4color(red)(+4)=-6color(red)(+4)

x=-2