If the supply function for a commodity is given by  p = q^2 and function is given by
P = -20q + 2500 find the point of market equilibrium.

To find the market equilibrium, we need to determine the point at which supply equals demand. In other words, we solve for \( q \) where the supply function \( p = q^2 \) equals the demand function \( P = -20q + 2500 \).

### Step 1: Set supply equal to demand
\[
q^2 = -20q + 2500
\]

### Step 2: Rearrange the equation
Bring all terms to one side:
\[
q^2 + 20q - 2500 = 0
\]

### Step 3: Solve the quadratic equation
We can solve this quadratic equation using the quadratic formula:
\[
q = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \( q^2 + 20q - 2500 = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = 20 \)
- \( c = -2500 \)

Substitute these into the quadratic formula:
\[
q = \frac{-20 \pm \sqrt{(20)^2 - 4(1)(-2500)}}{2(1)}
\]
\[
q = \frac{-20 \pm \sqrt{400 + 10000}}{2}
\]
\[
q = \frac{-20 \pm \sqrt{10400}}{2}
\]
\[
q = \frac{-20 \pm 102}{2}
\]

### Step 4: Find the two possible solutions
\[
q_1 = \frac{-20

If the supply function for a commodity is given by p = q^2 and the demand function is given by P = -20q + 2500, find the point of market equilibrium.

Find the market equilibrium where the supply function p = q^2 equals the demand function P = -20q + 2500. This detailed guide explains how to solve the resulting quadratic equation, providing a step-by-step approach for students in Grades 9-12.

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