Question

Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4

Answer 1

4x2 - 7x = 3x + 24
 First we rewrite the quadratic equation:
 4x2 - 7x - 3x - 24 = 0
 4x2 - 10x - 24 = 0
 The solutions to the quadratic equation in this case are:
 x1 = 4
 x2 = -1.5
 Answer:
 x = -3/2
 x = 4

Answer 2

Answer:

Given the equation: $4x^2-7x = 3x+24$

rewrite the above equation as: $4x^2-7x-3x-24=0$

Like terms are those whose variables are same.

Combine like terms :

$4x^2-10x-24=0$ ....[1]

Now, to solve the above quadratic equation:

For quadratic equation: $ax^2+bx+c=0$ where a,b, and c are constant.

then the solutions are:  

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$              ...[2]

in equation [1], the values of a= 4, b=-10 and c= -24.

then, by putting these in the [2] we get,

$x_{1,2}=\frac{-(-10)\pm\sqrt{(-10)^2-4(4)(-24)}}{2\cdot 4}$

On solving we get,  the solutions are:

$x_{1}=-1.5=-\frac{3}{2}$ and $x_{2}=4$

Check :

By substituting the values of x= -1.5 and x=4 in equation  $4x^2-7x = 3x+24$ we have;

for x=-1.5

$4x^2-7x=3x+24$

$4(-1.5)^2-7(-1.5)=3(-1.5)+24$

$4(2.25)+10.5=-4.5+24$

9+10.5=19.5

19.5=19.

Similarly, for x=4

$4x^2-7x=3x+24$

$4(4)^2-7(4)=3(4)+24$

$4(16)-28=12+24$

64-28=36

36=36

Therefore, the only solution of the equation  $4x^2-7x = 3x+24$  is, x= -1.5 and x=4