Answer key for solving quadratic equations, showing factored forms and solutions for each problem.

It looks like you've uploaded an image of a completed worksheet titled *"Solving Quadratic Equations (A) Answers"*, which shows the solutions to 20 quadratic equations. The worksheet already includes the answers, factored forms, and solutions for each equation.

Since this is an answer key, it appears that the original task was likely to solve these quadratic equations, and now the solutions are provided.

Let me explain how to solve one of these problems step-by-step as an example, so you understand the method used in the worksheet.

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🔍 Example: Solve Problem #1

Equation:
$$
-8x^2 + 74x - 18 = 0
$$

#### Step 1: Factor out the GCF (if possible)
The coefficients are $-8$, $74$, and $-18$. They don't have a common factor other than 1, so we proceed directly to factoring.

But notice: the leading coefficient is negative. It's often easier to factor when the leading coefficient is positive, so let’s multiply both sides by $-1$:

$$
8x^2 - 74x + 18 = 0
$$

Now, look for two numbers that:
- Multiply to $8 \times 18 = 144$
- Add to $-74$

Try pairs of factors of 144:
- $-6$ and $-24$: $(-6)(-24) = 144$, $-6 -24 = -30$ → too small
- $-8$ and $-18$: $(-8)(-18) = 144$, $-8 -18 = -26$
- $-12$ and $-12$: $(-12)(-12) = 144$, $-12 -12 = -24$
- Try $-1$ and $-144$: too far apart

Wait — maybe use the AC method or try factoring directly.

Alternatively, the worksheet gives the factored form:

$$
-2(4x - 1)(x - 9) = 0
$$

Let’s verify this.

First, expand $-2(4x - 1)(x - 9)$:

Step 1: Expand $(4x - 1)(x - 9)$:
$$
= 4x(x) + 4x(-9) + (-1)(x) + (-1)(-9)
= 4x^2 - 36x - x + 9 = 4x^2 - 37x + 9
$$

Now multiply by $-2$:
$$
-2(4x^2 - 37x + 9) = -8x^2 + 74x - 18
$$

✔ Matches the original equation!

So the factored form is correct.

#### Step 2: Set each factor equal to zero
$$
-2(4x - 1)(x - 9) = 0
$$

Set each factor to zero:
- $4x - 1 = 0$ → $x = \frac{1}{4}$
- $x - 9 = 0$ → $x = 9$

✔ So the solutions are:
$$
x = \frac{1}{4},\ 9
$$

Which matches the answer on the sheet.

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✔ General Method for Solving Quadratic Equations

For any quadratic equation in the form:
$$
ax^2 + bx + c = 0
$$

You can solve using:
1. Factoring (if possible)
2. Quadratic Formula:
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$
3. Completing the square

In this worksheet, all equations were solved by factoring after simplifying (e.g., factoring out GCFs or adjusting signs).

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📌 Summary

This worksheet provides solutions to 20 quadratic equations. Each problem was solved by:
- Factoring the quadratic expression
- Setting each factor equal to zero
- Solving for $x$

If your goal was to check your work or learn how to solve such equations, here's what you should remember:

🔹 Always look for a GCF first
🔹 Use factoring by grouping or AC method if needed
🔹 If factoring is hard, use the quadratic formula
🔹 Check your answers by plugging them back into the original equation

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Would you like me to walk through another problem from the list (e.g., #5, #10, or #20) in detail? Or do you want help creating a similar worksheet or understanding a specific concept?