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

Answer:

$x=5+\sqrt{12}$

or

$x=5-\sqrt{12}$

Step-by-step explanation:

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

$x^2-10x=-13$

$x^2-10x+(\frac{10}{2})^2 =-13+(\frac{10}{2})^2$

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

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

Factor.

$(x-5)^2=12$

Extract the square root.

$x-5=\frac{+}{} \sqrt{12}$

Add 5

$x=5+\sqrt{12}$

or

$x=5-\sqrt{12}$