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

Answer:

$x= \frac{7}{4},-1$  is the required solution.

Step-by-step explanation:

We have been given the equation:

$\frac{3}{2}\cdot \frac{x+7}{2}=x^2$

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

After first step of simplification we get:

$\frac{3x}{2}+\frac{7}{2}=2x^2$

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

$x=\frac{-b\pm\sqrt{D}}{2a}$

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

$x=\frac{-(-3)\pm\sqrt{121}}{2\cdot 4}$

$x= \frac{3\pm\11}{8}$

$\Rightarrow \frac{14}{8},\frac{-8}{8}$

$\Rightarrow \frac{7}{4},-1$