Question

Solve |x+ 3|- 1 = (x + 2)^2 by graphing. The solutions are x = and x =

Answer 1

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.