Question

Complete the square to solve the quadratic equation.
x?+8x-14=0
Step 1: Use inverse operations to isolate the constant.
Step 2: Add the same number to both sides to complete the square.
Step 3: Factor the perfect square trinomial.
x2+8x=
• Answer
x2+8x+
=14+
What is (2)}? Answer !
x+8x+16=14+16
Simplify.
1=30
What is in the blank?
Answer
Step 4: Take the square root of both sides.
x+4=
Answer
Step 5: Solve for x.
X=
• Answer
::16
::14
::÷30
:x+4
::-4+/30 and -4-J30

Answer 1

Let's complete the square step by step for the quadratic equation \( x^2 + 8x - 14 = 0 \).

### Step 1: Isolate the constant
We first want to move the constant term (-14) to the other side of the equation:

\[
x^2 + 8x = 14
\]

### Step 2: Complete the square
Next, we need to add the square of half the coefficient of \( x \) to both sides. The coefficient of \( x \) is 8. Half of 8 is 4, and squaring it gives us \( 4^2 = 16 \).

Add 16 to both sides:

\[
x^2 + 8x + 16 = 14 + 16
\]

### Step 3: Factor the perfect square trinomial
The left side can be factored as:

\[
(x + 4)^2 = 30
\]

### Step 4: Take the square root of both sides
Now, we take the square root of both sides:

\[
x + 4 = \pm \sqrt{30}
\]

### Step 5: Solve for \( x \)
Finally, solve for \( x \) by isolating it:

\[
x = -4 \pm \sqrt{30}
\]

### Summary
The complete solution for the quadratic equation \( x^2 + 8x - 14 = 0 \) is:

\[
x = -4 + \sqrt{30} \quad \text{or} \quad x = -4 - \sqrt{30}
\]