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.

Question

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