Complete the square to identify the two values that solve the quadratic equation x^2 + 8x = 9.

Question

x = ?

Answer 1

To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, follow these steps:

1. Move the constant term to the other side of the equation:

   \[ x^2 + 8x - 9 = 0 \]

2. Isolate the \( x \) terms:

   \[ x^2 + 8x = 9 \]

3. Complete the square. Take half of the coefficient of \( x \) (which is 8), square it, and add it to both sides of the equation. Half of 8 is 4, and \( 4^2 = 16 \):

   \[ x^2 + 8x + 16 = 9 + 16 \]

4. Simplifying gives:

   \[ x^2 + 8x + 16 = 25 \]

5. The left side can be factored as a perfect square:

   \[ (x + 4)^2 = 25 \]

6. Now take the square root of both sides:

   \[ x + 4 = \pm 5 \]

7. This gives us two equations to solve for \( x \):

   • \( x + 4 = 5 \)
   • \( x + 4 = -5 \)

8. Solving these:

   • For \( x + 4 = 5 \): \[ x = 5 - 4 = 1 \]

   • For \( x + 4 = -5 \): \[ x = -5 - 4 = -9 \]

Thus, the two values that solve the quadratic equation \( x^2 + 8x = 9 \) are:

\[ x = 1 \quad \text{and} \quad x = -9 \]

Answer 2

Theres only one answer

Answer 3

I apologize for any confusion. However, the equation \(x^2 + 8x = 9\) actually has two solutions, which are derived through completing the square or using the quadratic formula.

Let me clarify:

1. Start with the original equation: \[ x^2 + 8x - 9 = 0 \]

2. Using completing the square, we transformed it into: \[ (x + 4)^2 = 25 \]

3. Taking square roots, we found: \[ x + 4 = 5 \quad \text{or} \quad x + 4 = -5 \]

which leads to the solutions:

• \( x = 1 \)
• \( x = -9 \)

Thus, the two solutions are \(x = 1\) and \(x = -9\).

If you meant that you are looking for just one of the answers, you can choose either \(1\) or \(-9\). Please clarify your question, and I'll be happy to assist!