Solve for x in the equation x squared minus 4 x minus 9 = 29.
x = 2 plus-or-minus StartRoot 42 EndRoot
x = 2 plus-or-minus StartRoot 33 EndRoot
x = 2 plus-or-minus StartRoot 34 EndRoot
x = 4 plus-or-minus StartRoot 42 EndRoot

Let's solve the equation step by step:

The equation is:

\[
x^2 - 4x - 9 = 29
\]

### Step 1: Move all terms to one side of the equation
Subtract 29 from both sides:

\[
x^2 - 4x - 9 - 29 = 0
\]

This simplifies to:

\[
x^2 - 4x - 38 = 0
\]

### Step 2: Solve using the quadratic formula

The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \(x^2 - 4x - 38 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -4\)
- \(c = -38\)

### Step 3: Calculate the discriminant

The discriminant is \(b^2 - 4ac\):

\[
(-4)^2 - 4(1)(-38) = 16 + 152 = 168
\]

### Step 4: Substitute the values into the quadratic formula

Now substitute into the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{168}}{2(1)}
\]

This simplifies to:

\[
x = \frac{4 \pm \sqrt{168}}{2}
\]

### Step 5: Simplify the square root

\[
\sqrt{168} \approx 12.96
\]

So the equation becomes:

\[
x = \frac{4 \pm 12.96}{2}
\]

### Step 6: Final solutions

Now, calculate the two possible values for \(x\):

1. \(x = \frac{4 + 12.96}{2} = \frac{16.96}{2} \approx 8.48\)
2. \(x = \frac{4 - 12.96}{2} = \frac{-8.96}{2} \approx -4.48\)

So the solutions are approximately \(x = 8.48\) and \(x = -4.48\).

### Answer based on choices:
The correct answer from the options is:

\[
x = 2 \pm \sqrt{42}
\]

Would you like further details or have any questions?

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Here are some follow-up questions:

1. How can you derive the quadratic formula?
2. What is the discriminant, and how does it affect the number of solutions?
3. What are the steps to simplify square roots in quadratic equations?
4. How do you check the solutions of a quadratic equation?
5. Can you factor the equation instead of using the quadratic formula?

**Tip:** Always check if factoring is easier before using the quadratic formula!

Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot

Learn how to solve the quadratic equation x² - 4x - 9 = 29 using the quadratic formula. This detailed solution explains how to calculate the discriminant and derive the correct roots. Perfect for students in Grades 9-10 learning about quadratic equations.

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