https://file.aiquickdraw.com/mathbot/file/1725498780280ztc5ua3l.jpg

It seems the text extraction from the image wasn't fully successful. Based on visual inspection of the image, the equation is:

\[
4(5x - 10)^2 - 34 = -33
\]

Let me go ahead and solve this equation for \( x \).

### Steps:
1. Add 34 to both sides of the equation:
   \[
   4(5x - 10)^2 = 1
   \]

2. Divide both sides by 4:
   \[
   (5x - 10)^2 = \frac{1}{4}
   \]

3. Take the square root of both sides:
   \[
   5x - 10 = \pm \frac{1}{2}
   \]

4. Solve the two resulting linear equations:
   \[
   5x - 10 = \frac{1}{2} \quad \text{or} \quad 5x - 10 = -\frac{1}{2}
   \]

Now, let's continue solving this.The solutions to the equation \( 4(5x - 10)^2 - 34 = -33 \) are:

\[
x = 2.1 \quad \text{or} \quad x = 1.9
\]

Would you like further details on any step or have any other questions?

Here are some related questions to expand your understanding:
1. How would the solution change if the constant on the right side was different, such as \(-35\)?
2. What would happen if the expression inside the square was linear instead of quadratic?
3. Can you solve similar quadratic equations using the quadratic formula instead of factoring?
4. How does taking the square root of both sides of an equation affect the possible solutions?
5. How would you approach solving this equation graphically?

**Tip**: Always check both solutions by substituting them back into the original equation to confirm accuracy.

Solve the equation: 4(5x - 10)^2 - 34 = -33

Learn how to solve the quadratic equation 4(5x - 10)^2 - 34 = -33 with detailed step-by-step instructions. This problem covers concepts of squaring binomials and solving linear equations, suitable for high school algebra students.

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