solve equation using square

Question

how do I solve by completing the square, round to the nearest hundredth?

 

    x^2 - 3x =4

 

 

 

I have this as a starter   x^2 - 3x + 9/4  = 4  + 9/4

Answer 1

x^2 - 3x = 4

 

We know (x - h)^2 = x^2 - 2hx + h^2 ;

so if we force the pattern on the right,

we can replace it with the pattern on the left:

 

x^2 - 2(3/2)x + (3/2)^2 = 4 + (3/2)^2

 

(x - 3/2)^2 = 4 + 9/4 = 25/4

 

(x - 3/2)^2 = (5/2)^2

 

[Note that at this point we can easily see

the Vertex Form: (x - 3/2)^2 - 25/4 = 0,

with vertex at (3/2,-25/4).]

 

Now take square root of both sides, 

remembering that √(s^2) = |s|:

 

|x - 3/2| = 5/2

 

x - 3/2 = ±5/2

 

x = 3/2 ± 5/2

 

x = (3 ± 5)/2 = 4 or -1

Answer 2

Hi again L;

x² - 3x =4

Let's move the 4 from the right to the left...

x²-3x-4=0

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must add-up to -3x

LAST must be (4)(1) or (1)(4) or (2)(2) and one number must be negative such that the result is -4.

(x+1)(x-4)=0

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(-4)=-4x

INNER...(1)(x)=1x=x

LAST...(1)(-4)=-4

x²-4x+x-4=0

x²-3x-4=0

(x+1)(x-4)=0

Either or both parenthetical equations must equal zero...

x+1=0

x=-1

x-4=0

x=4