Use completing the square to solve for x in the equation (x + 7) (x minus 9) = 25.
x = –4 or 6
x = –2 or 14
x = 1 plus-or-minus StartRoot 89 EndRoot
x = 1 plus-or-minus StartRoot 87 EndRoot

To solve the equation \((x + 7)(x - 9) = 25\) using the method of completing the square, let's follow the steps.

### Step 1: Expand the expression
First, expand the left-hand side:

\[
(x + 7)(x - 9) = x^2 - 9x + 7x - 63 = x^2 - 2x - 63
\]

So the equation becomes:

\[
x^2 - 2x - 63 = 25
\]

### Step 2: Move the constant to the other side
Add \(63\) to both sides:

\[
x^2 - 2x = 25 + 63 = 88
\]

### Step 3: Complete the square
To complete the square, take half of the coefficient of \(x\) (which is \(-2\)) and square it:

\[
\left(\frac{-2}{2}\right)^2 = 1
\]

Add \(1\) to both sides of the equation:

\[
x^2 - 2x + 1 = 88 + 1 = 89
\]

Now the left-hand side is a perfect square:

\[
(x - 1)^2 = 89
\]

### Step 4: Solve for \(x\)
Take the square root of both sides:

\[
x - 1 = \pm \sqrt{89}
\]

Finally, solve for \(x\):

\[
x = 1 \pm \sqrt{89}
\]

So the solution is:

\[
x = 1 \pm \sqrt{89}
\]

This matches the option:
\[
x = 1 \pm \sqrt{89}
\]

### Final Answer: 
\[
\boxed{x = 1 \pm \sqrt{89}}
\]

Would you like further details or have any questions about the steps?

Here are 5 related questions for further practice:
1. Solve \(x^2 - 6x - 7 = 0\) by completing the square.
2. Factor the quadratic expression \(x^2 - 4x - 45 = 0\).
3. Solve \(x^2 + 10x - 4 = 0\) by completing the square.
4. What are the steps to complete the square for \(x^2 + 8x + 16 = 9\)?
5. Solve the equation \(x^2 - 5x + 2 = 10\) using completing the square.

**Tip:** Completing the square is useful not only for solving quadratic equations but also for converting equations into the vertex form of a parabola!

Use completing the square to solve for x in the equation (x + 7)(x - 9) = 25. x = –4 or 6 x = –2 or 14 x = 1 plus-or-minus StartRoot 89 EndRoot x = 1 plus-or-minus StartRoot 87 EndRoot

Learn how to solve the quadratic equation (x + 7)(x - 9) = 25 by completing the square. Follow the step-by-step process to simplify and solve for x, including key algebraic concepts and formulas. Suitable for students in Grades 9-11.

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