https://file.aiquickdraw.com/mathbot/file/1726763628524klpgrq67.jpg

Let's go through the problem step by step to solve it by completing the square.

1. **Starting with the given equation**:
   \[
   x^2 - 8x + 4 = -3
   \]
   First, subtract 4 from both sides:
   \[
   x^2 - 8x = -7
   \]

2. **Now, complete the square**. Take half of the coefficient of \(x\), which is \(-8\), divide by 2 to get \(-4\), and then square it to get \(16\). Add 16 to both sides:
   \[
   x^2 - 8x + 16 = -7 + 16
   \]
   Simplifying:
   \[
   x^2 - 8x + 16 = 9
   \]

3. **Rewrite the left-hand side as a perfect square**:
   \[
   (x - 4)^2 = 9
   \]

4. **Solve for \(x\)** by taking the square root of both sides:
   \[
   x - 4 = \pm 3
   \]
   This gives two solutions:
   \[
   x - 4 = 3 \quad \text{or} \quad x - 4 = -3
   \]

5. **Solve for \(x\)** in both cases:
   \[
   x = 7 \quad \text{or} \quad x = 1
   \]

Thus, the solutions are \(x = 7\) or \(x = 1\).

---

Would you like more details about any step? Here are some related questions you might find helpful:

1. How do you derive the value to add when completing the square?
2. Why do we take the square root of both sides when solving?
3. How do you recognize when to complete the square vs using other methods?
4. Can this method be applied to equations with larger coefficients or constants?
5. How can you verify that your solutions are correct?

**Tip**: Always check your final answers by substituting them back into the original equation to ensure they satisfy it!

Solve by completing the Square for the equation x^2 - 8x + 4 = -3.

Learn how to solve the quadratic equation x^2 - 8x + 4 = -3 by completing the square. This problem demonstrates key algebraic techniques, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation