4x^2 -12x=7

Question

Solve algebraically for x

Answer 1

4x^2-12x=7

4x^2-12x-7=0

 

Now we have several ways to proceed.

 

1/ Use the quadratic formula where the roots of ax^2+bx+c=0 are (-b+/-sqrt(b^2-4ac))/2a

In the question a=4, b=-12 and c=-7 so  x=(12+/-sqrt(144+4*4*7))/8=7/2 0r -1/2.

 

2/ Complete the square:

4(x^2-3x-7/4)=0

(x-3/2)^2-9.4-7/4=0   (dividing both sides by 4 removes the coefficient of x^2)

(x-3/2)^2=4 so x=+/-2+3/2 , x=7/2 or -1/2

 

3) Try to factorize:

(2x  ?  1(2x ?  7)  Which signs can give us -12x?  The fact that -7 is negative means that one must be positive, the

other negative,  Since -12x is negative, we should associate the negative sign with the larger contributory product.

I.e. 2x*(-7)=-14x and by inspection (+1)*2x=2x so we do indeed have net -12x.

(2x+1)(2x-7)=0  So 2x+1=0 or 2x-7=0 etc.

Answer 2

4x^2-12x=7

4x^2-12x-7

4*7=2*2*7=(2)*(2*7) and 14-2=12, the coefficient of the middle term

(2x    7)(2x    1) so far...

(2x-7)(2x+1)=0

2x-7=0

2x=7

x=7/2

2x+1=0

2x=-1

x=-1/2