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4 votes
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?

2 Answers

5 votes
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!
User Pranjal Sahu
by
8.5k points
2 votes

Answer:


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

User Joncys
by
8.9k points

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