https://file.aiquickdraw.com/mathbot/file/1726843421032u5qcpu1m.jpg

The equation in the image appears to be:

\[
18x^2 - 8x + 15 = 16x^2 - 8x + 15
\]

We need to solve this equation for \( x \). Here's the step-by-step solution:

### Step 1: Subtract both sides by \( 16x^2 - 8x + 15 \)
\[
(18x^2 - 8x + 15) - (16x^2 - 8x + 15) = 0
\]

Simplifying:
\[
18x^2 - 8x + 15 - 16x^2 + 8x - 15 = 0
\]

### Step 2: Combine like terms
\[
(18x^2 - 16x^2) + (-8x + 8x) + (15 - 15) = 0
\]
\[
2x^2 = 0
\]

### Step 3: Solve for \( x \)
Divide both sides by 2:
\[
x^2 = 0
\]

Take the square root of both sides:
\[
x = 0
\]

### Solution:
The solution to the equation is \( x = 0 \).

Would you like more details or have any questions?

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Here are five questions to expand on this concept:
1. How would the solution change if the constant terms were different?
2. What happens if you encounter complex roots in a quadratic equation?
3. Can you solve a similar equation where the quadratic terms are negative?
4. How can we solve this equation graphically?
5. What if there are higher degree polynomials involved in the equation?

**Tip:** Always simplify both sides of the equation as much as possible before solving!

Find the solution set of 18x^2 - 8x + 15 = 16x^2 - 8x + 15.

This detailed guide helps you solve the quadratic equation 18x^2 - 8x + 15 = 16x^2 - 8x + 15 through simplification and step-by-step reasoning. Ideal for students in Grades 8-10, covering algebraic concepts and the use of the fundamental theorem of algebra.

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