Question

What are the solutions to the equation 4x2+3x=24-x

Answer 1

Answer:

x=2                x=-3

Step-by-step explanation:

4x2+3x=24-x

Subtract 24 from each side

4x^2 +3x -24 = 24-24 -x

4x^2 +3x -24 = -x

Add x to each side

4x^2 +3x+x -24 = -x+x

4x^2 +4x -24 = 0

Factor out a 4

4(x^2 +x -6) = 0

Divide by 4

x^2 +x -6 =0

Factor

What 2 numbers multiply to -6 and add to 1

-2*3 = -6

-2+3 =1

(x-2) (x+3) =0

Using the zero product property

x-2 =0            x+3 =0

x-2+2=0+2    x+3-3=0-3

x=2                x=-3

Answer 2

Answer:x=-3 , x = 2

Step-by-step explanation:

First move the expression ( 24-x) to the left.

This gives us 4x^2+3x+24-x.

Collect the like terms which gives us 4x^2+4x+24

4x^2+4x-24 = 0.  Divide both sides by 4.

x^2 + x-6 = 0

Factorise the expression so you get (x+3)(x-2)=0

Solve the equations x+3 = 0 and x-2=0

The final solutions are x=-3 and x=2.