Question

X^2 - 72 = 6x
how to complete the square?

Answer 1

Answer:

Step-by-step explanation
x^2-6×-72= O
(b/2)^2= b, -6:(-6/2)^2=(-3)^2= 9
x^2-6x+(-3)^2-(-3)^2-72=0
(x-3)^2-9-72=0
(x-3)^2-81= 0
(x -3)^2= 81, x-3= ±9
x= +9+3= 12
x= -9+3=-6
: X= 12 , X= -6

Answer 2

x = 12 and x = -6

Explanation:

First subtract 6x on both sides to get a 2nd degree polynomial equal to zero:

`x^2-6x-72=0`

To complete the square, the formula is to divide 'b' by 2 and square the result. The general form for a 2nd degree polynomial of the variable 'x' is as follows:

`ax^2+bx+c=0`

For your case, b = 6. Therefore, the term that must be added and subtracted to our equation is:

`(6/2)^2=3^2=9`

Add and subtract 9 to our equation to get:

`x^2-6x+9-9-72=0`

The first three terms form a perfect square, we have:

`(x^2-6x+9)-9-72=0`

`(x^2-6x+9)-81=0`

What multiplies to equal 9 but adds to equal -6? That would be -3 and -3. Therefore:

`(x-3)^2-81=0`

Add 81 to both sides to get:

`(x-3)^2=81`

We want to take the square root, but recall a square root has a positive and negative branch. Therefore we have two solutions:

`x-3=9`

`x-3=-9`

`x=12`

`x=-6`