Question

What is the set of all solutions to the equation \sqrt{x + 2}= {-x} x+2 ​ =−xsquare root of, x, plus, 2, end square root, equals, minus, x ?

Answer 1

Answer:

$x = 2$ or $x = -1$

Step-by-step explanation:

Given

$\sqrt{x + 2}= {-x}$

Required

Find the possible values fo x

$\sqrt{x + 2}= {-x}$

Square both sides

$( \sqrt{x + 2})^2= ({-x})^2$

$x + 2 = x^2$

Equate to 0

$x^2 - x - 2 = 0$

Expand

$x^2 + x -2x - 2 = 0$

Factorize:

$x(x + 1) - 2(x + 1) = 0$

$(x -2)(x +1) = 0$

Split:

$x - 2 = 0$ or $x + 1 = 0$

$x = 2 + 0$ or $x = 0-1$

$x = 2$ or $x = -1$