Question

An equation is shown below:

3 over 2 multiplied by x plus 7 over 2 equals 2 to the power of x

What is the solution to the equation?

Answer 1

Let X = 3:

3x/2 + 7/2 = 2^x.
3*3/2 + 7/2 = 2^3.
9/2 + 7/2 = 8.
16/2 = 8.
8 = 8.

So X = 3 is the answer my friend!

Answer 2

`x= (7)/(4),-1` is the required solution.

Explanation:

We have been given the equation:

`(3)/(2)\cdot (x+7)/(2)=x^2`

We will solve for x to get the solution of the equation

After first step of simplification we get:

`(3x)/(2)+(7)/(2)=2x^2`

Now, distribute the parenthesis on left hand side of the equation:

`3x+7=4x^2`

`4x^2-3x-7=0`

We will solve the above quadratic equation by discriminant rule

`x=(-b\pm√(D))/(2a)`

Where,
`D=b^2-4ac`

We will compare the equation with general quadratic equation:

`ax^2+bx+c=0`

Here, a=4,b= -3 and c=-7 on substituting the values we get:

`D=(-3)^2-4(4)(-7)`

`D=9+112=121`

Now for x

`x=(-(-3)\pm√(121))/(2\cdot 4)`

`x= (3\pm\11)/(8)`

`\Rightarrow (14)/(8),(-8)/(8)`

`\Rightarrow (7)/(4),-1`