#### Question

In the following, determine whether the given values are solutions of the given equation or not:

2x^{2} - x + 9 = x^{2} + 4x + 3, x = 2, x =3

#### Solution

We have been given that,

2x^{2} - x + 9 = x^{2} + 4x + 3

2x^{2} - x + 9 - x^{2} - 4x - 3 = 0

x^{2} - 5x + 6 = 0, x = 2, x = 3

Now if x = 2 is a solution of the equation then it should satisfy the equation.

So, substituting x = 2 in the equation, we get

x^{2} - 5x + 6

= (2)^{2} - 5(2) + 6

= 4 - 10 + 6

= 0

Hence x = 2 is a solution of the given quadratic equation

Also, if x = 3 is a solution of the equation then it should satisfy the equation.

So, substituting x = 3 in the equation, we get

x^{2} - 5x + 6

= (3)2 - 5(3) + 6

= 9 - 15 + 6

= 0

Hence x = 3 is a solution of the quadratic equation.

Therefore, from the above results we find out that both x = 2 and x = 3 are solutions of the quadratic equation.