Fill in the steps to complete the square:

Question

x 2 + 12 - 14 = 0
x^2 + 12x = 14
x^2 + 12x + blank = 14 + blank
We factor and simplify to get: ( x + 6^2) = blank
At this point , we need to blank
After that point, we need to blank
After that is done, we will have: blank = blank
We get isolate the veritable by: blank
Final answers are: blank
(x +6)^2
112
Squa.
Re both sides of the equation
-22
+ with line under it ^36
-12 & 0
Take the square root of both sides up equation
+ with line under it ^50
Subtracting twelve from both sides of the equation
-6 + with line under it ^36
(x + 12)^2
Subtracting six from both sides of the equation
100
^x + 12
36
17
144
^x + 6
x + 12
+with line under it 12
12
x+ 6

Answer 1

To complete the square for the equation \(x^2 + 12x - 14 = 0\), follow these steps:

1. Start with the equation: \(x^2 + 12x - 14 = 0\)

2. Rearrange it to form: \(x^2 + 12x = 14\)

3. To complete the square, we need to add a value to both sides. This value is derived from taking half of the coefficient of \(x\) (which is 12), squaring it, and then adding it to both sides: Half of 12 is 6, and squaring it gives us \(6^2 = 36\).

4. Fill in the blanks: \(x^2 + 12x + 36 = 14 + 36\)

5. This simplifies to: \((x + 6)^2 = 50\)

6. To solve for \(x\), we need to take the square root of both sides: \(\sqrt{(x + 6)^2} = \pm \sqrt{50}\)

7. This results in: \(x + 6 = \pm 5\sqrt{2}\)

8. Finally, isolate \(x\): \(x = -6 \pm 5\sqrt{2}\)

Therefore, the final answers are:

• \(x_1 = -6 + 5\sqrt{2}\)
• \(x_2 = -6 - 5\sqrt{2}\)

Here is the completed summary of the process:

1. Start with \(x^2 + 12 - 14 = 0\).
2. Rearrange to \(x^2 + 12x = 14\).
3. Complete the square: \(x^2 + 12x + 36 = 14 + 36\).
4. Factor: \((x + 6)^2 = 50\).
5. Take the square root: \(x + 6 = \pm \sqrt{50}\).
6. Isolate \(x\): \(x = -6 \pm 5\sqrt{2}\).
7. Solutions: \(x_1 = -6 + 5\sqrt{2}\), \(x_2 = -6 - 5\sqrt{2}\).