Question

Given f(x)=(x+3)^2 and g(x)=|x+1| , which value is a solution to the equation f(x)=g(x) ?

A. –5
B. 5
C. 4
D. -1

help asap pls

Answer 1

A)
`x = -5`

Explanation:

`(x + 3)^2 = | x + 1 |\\\to x^2 + 6x + 9 = | x + 1|`

Case 1: x + 1 is positive

`x^2 + 6x + 9 = x + 1\\\to x^2 + 5x + 8 = 0\\\to \text{No solutions.}`

Case 2: x + 1 is negative

`-x^2 - 6x - 9 = x + 1\\\to 0 = x^2 + 7x + 10\\\to 0 = (x + 5)( x + 2)\\\to x = -5 \text{ or } x = -2`