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

We are tasked with solving the equation \((x + 7)(x - 9) = 25\) by completing the square. Let’s go through the steps.

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

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

Now, the equation is:

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

### Step 2: Move the constant term to the other side
Add \(63\) to both sides to isolate the quadratic and linear terms:

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

\[
x^2 - 2x = 88
\]

### Step 3: Complete the square
To complete the square, we need to add \(\left(\frac{-2}{2}\right)^2 = 1\) to both sides of the equation:

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

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

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

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

Finally, solve for \(x\):

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

Thus, the solution is:

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

The correct answer is:

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

---

Do you want more details or have any questions? Here are five related questions:

1. How do you complete the square for a quadratic equation?
2. Can completing the square be used for any quadratic equation?
3. Why do we add and subtract the same value when completing the square?
4. How does completing the square relate to the quadratic formula?
5. What are the applications of completing the square in solving word problems?

**Tip:** Completing the square is helpful when graphing parabolas, as it can easily reveal the vertex form of a quadratic equation.

Use completing the square to solve for x in the equation (x + 7)(x - 9) = 25.

Learn how to solve the quadratic equation (x + 7)(x - 9) = 25 using the completing the square method. This step-by-step solution covers key algebraic concepts like expanding, isolating terms, and completing the square. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation