Question

Someone please help me with my problems for math

Answer 1

The first option: (x + 6)² = x² + 12x +36

x = √14 - 6, -√14 - 6

With rounded decimals: x = -2.26, -9.74

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:

• 12x = 2xy
• 6x = xy
• y = 6

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