Answer:
The first option: (x + 6)² = x² + 12x +36
x = √14 - 6, -√14 - 6
With rounded decimals: x = -2.26, -9.74
Step-by-step explanation:
Hey there!
In the equation, we can see that x² + 12x is part of a square of a sum
A square of a sum can be represented by this equation:
(x + y)² = x² + 2xy + y²
Here, 12x = 2xy:
Now we can complete the square:
- x² + 12x + 22 = 0
- x² + 12x + 6² + 22 = 0 => add 36 to both sides(complete the square)
- x² + 12x + 36 + 22 = 36 => factor
- (x + 6)² + 22 = 36
- (x + 6)² = 14
- √(x + 6) = √14
- |x + 6| = √14
- x = √14 - 6, x = -√14 - 6
-Chetan k
