Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property.

x squared minus 8 x plus 16 equals 49x2−8x+16=49

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Part 1

The solution set is

StartSet nothing EndSetenter your response here.

​(Simplify your answers. Type exact​ answers, using radicals as needed. Type your answer in the form a​ +

bii.

Use a comma to separate answers as​ needed.)

Let's solve the quadratic equation step by step.

### Given equation:
\[ x^2 - 8x + 16 = 49 \]

### Step 1: Factor the perfect square trinomial on the left side.
Notice that \( x^2 - 8x + 16 \) can be factored as:
\[
(x - 4)^2 = 49
\]

### Step 2: Apply the square root property.
To solve the equation, take the square root of both sides:
\[
\sqrt{(x - 4)^2} = \pm \sqrt{49}
\]
This simplifies to:
\[
x - 4 = \pm 7
\]

### Step 3: Solve for \( x \).
Now, solve for \( x \) by adding 4 to both sides:

1. \( x - 4 = 7 \)
   \[
   x = 7 + 4 = 11
   \]

2. \( x - 4 = -7 \)
   \[
   x = -7 + 4 = -3
   \]

### Final Answer:
The solution set is:
\[
\{ -3, 11 \}
\]

Do you want more details or have any questions?

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1. What is a perfect square trinomial?
2. How do you identify a perfect square trinomial?
3. What is the square root property in algebra?
4. How can you verify the solutions to a quadratic equation?
5. What other methods can solve quadratic equations?
6. How do perfect squares relate to completing the square?
7. What is the significance of the ± symbol in the square root property?
8. What happens if the right side of the equation is not a perfect square?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation x^2 - 8x + 16 = 49 using factoring and the square root property. Detailed step-by-step solution provided. Suitable for students in Grades 7-9.

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