Question

Solve the equation x squared plus 4 x equals 18 by completing the square. Round decimal answers to the nearest tenth. Enter the answers in the boxes.

Response area with 8 text input boxes
x squared plus 4 x equals 18

x squared plus 4 x plus
equals 18 plus


left-parenthesis x plus
right-parenthesis squared equals


x plus
equals plus or minus


x equals
and negative

Answer 1

To solve the equation \( x^2 + 4x = 18 \) by completing the square, let's go through the steps.

1. Start with the original equation:
\[
x^2 + 4x = 18
\]

2. Move the constant to the other side:
\[
x^2 + 4x - 18 = 0
\]

3. To complete the square, take half of the coefficient of \( x \) (which is 4), square it, and add it to both sides. Half of 4 is 2, and squaring it gives \( 2^2 = 4 \).

4. Rewrite the equation as:
\[
x^2 + 4x + 4 = 18 + 4
\]
This simplifies to:
\[
x^2 + 4x + 4 = 22
\]

5. Now, write the left-hand side as a squared term:
\[
(x + 2)^2 = 22
\]

6. Take the square root of both sides:
\[
x + 2 = \pm \sqrt{22}
\]

7. Solve for \( x \):
\[
x = -2 \pm \sqrt{22}
\]

8. Now calculate \( \sqrt{22} \), which is approximately 4.690 (rounding to the nearest tenth gives 4.7). Thus:
\[
x = -2 + 4.7 \quad \text{and} \quad x = -2 - 4.7
\]
This gives:
\[
x = 2.7 \quad \text{and} \quad x = -6.7
\]

Now, we can fill in the response area based on these calculations:

- **x squared plus 4 x plus**: 4
- **equals 18 plus**: 4
- **left-parenthesis x plus**: 2
- **right-parenthesis squared equals**: 22
- **x plus**: 2
- **equals plus or minus**: 4.7
- **x equals**: 2.7
- **and negative**: 6.7

So, the final answers are:

- x squared plus 4 x plus: **4**
- equals 18 plus: **4**
- left-parenthesis x plus: **2**
- right-parenthesis squared equals: **22**
- x plus: **2**
- equals plus or minus: **4.7**
- x equals: **2.7**
- and negative: **6.7**