Question

Solve the equation by Completing the Square
x2 – 10x + 13 = 0

Answer 1

X^2 -10x = -13
c= ( -10/2)^2
= (-5)^2
= 25

x^2 -10x+25= -13+25
x^2-10x+25= 12
(x-5) (x-5) =12
x-5 =12
x-5+5=12+5
x= 17

Answer 2

`x=5+√(12)`

or

`x=5-√(12)`

Explanation:

`x^2-10x+13=0`

`x^2-10x=-13`

`x^2-10x+((10)/(2))^2 =-13+((10)/(2))^2`

`x^2-10x+(5)^2=-13+(5)^2`

`x^2-10x+25=-13+25\\x^2-10x+25=12`

Factor.

`(x-5)^2=12`

Extract the square root.

`x-5=\frac{+}{} √(12)`

Add 5

`x=5+√(12)`

or

`x=5-√(12)`