Answer:
Given equation: [tex]x^2-8x =39[/tex]
when we complete the square , we take half of the value of 8 , then square it, and added to the left sides, we get;
[tex]x^2-8x+4^2 = 39 +4^2[/tex]
∵8 is the value [tex](\frac{8}{2})^2[/tex]
Notice that, we add this both sides so that it maintains the equality.
then;
[tex]x^2-8x+4^2 = 39 +4^2[/tex]
[tex](x-4)^2 = 39 + 16[/tex] [ [tex](a-b)^2 = a^2-2ab+b^2[/tex] ]
Simplify:
[tex](x-4)^2 =55[/tex]
The number must be added to complete the square is, [tex]4^2 = 16[/tex]
Answer:
The number must be added to complete the square is 16
Step-by-step explanation:
It is given that,
x^2 - 8x = 39 ------(1)
The quadratic equation is of the form ax^2 + bx + c =0
To complete the square we have to add (b/2)^2 and subtract (b/2)^2
Therefore the eq (1) becomes
here b= -8, so we have to add (8/2)^2 = 4^2 = 16
Therefore the number is 16
To find x
x^2 - 8x = 39
Add 16 to both sides
x^2 - 8x +16 = 39 + 16
(x - 4)^2 = 55
x - 4 = √55
x = √55 -4
