9514 1404 393
Answer:
x = -2, x = -1
Step-by-step explanation:
A graphing calculator solves this nicely, as shown in the attachment.
x = -2, x = -1
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The given equation resolves to two equations.
x+3 < 0
-(x +3) -1 = (x +2)^2
x^2 +5x +7 = 0
Checking the discriminant, we find ...
b^2 -4ac = (5)^2 -4(1)(7) = 25 -28 = -3
There are only complex solutions to this equation.
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x+3 ≥ 0
x +3 -1 = (x +2)^2
(x +2)^2 -(x +2) = 0 . . . .subtract x+2
(x +2)(x +2 -1) = 0 . . . . . factor
Solutions are values of x that make these factors zero.
x +2 = 0 ⇒ x = -2
x +1 = 0 ⇒ x = -1
Domain Check
x +3 = -2 +3 = 1 > 0 . . . . as required.
