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The equation provided is:

\[
(2x - 1)(5x + 3) = x + 8
\]

Let's solve this step-by-step.

### Step 1: Expand the Left Side
Using the distributive property, expand \((2x - 1)(5x + 3)\):

\[
(2x)(5x) + (2x)(3) - (1)(5x) - (1)(3)
\]

This simplifies to:

\[
10x^2 + 6x - 5x - 3
\]

Combine like terms:

\[
10x^2 + x - 3
\]

So the equation now reads:

\[
10x^2 + x - 3 = x + 8
\]

### Step 2: Move All Terms to One Side
Subtract \(x\) and \(8\) from both sides to set the equation to zero:

\[
10x^2 + x - 3 - x - 8 = 0
\]

This simplifies to:

\[
10x^2 - 11 = 0
\]

### Step 3: Solve the Quadratic Equation
Now we have a quadratic equation:

\[
10x^2 - 11 = 0
\]

Rewrite this as:

\[
10x^2 = 11
\]

Divide both sides by 10:

\[
x^2 = \frac{11}{10} = 1.1
\]

Take the square root of both sides to solve for \(x\):

\[
x = \pm \sqrt{1.1}
\]

Calculating the square root of 1.1 to two decimal places:

\[
x \approx \pm 1.05
\]

### Solution
The solutions are:

\[
x \approx 1.05 \quad \text{and} \quad x \approx -1.05
\]

Would you like a detailed explanation of any step?

---

Here are some related questions:

1. How do you verify solutions in a quadratic equation?
2. What are the different methods to solve quadratic equations?
3. How does factoring compare to using the quadratic formula?
4. When should you complete the square instead of other methods?
5. How do you handle equations where the discriminant is negative?

**Tip:** For accuracy, always double-check your work after each algebraic transformation!

Solve (2x - 1)(5x + 3) = x + 8. Give your answers correct to 2 decimal places.

Learn how to solve the quadratic equation (2x - 1)(5x + 3) = x + 8. This problem involves expanding binomials, forming a quadratic equation, and applying the quadratic formula. Suitable for students in Grades 10-12.

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