What is the answer to (-x-1)^2-3=-1-sqrt(x+3) ?

The answer to (-x-1)^2-3=-1-sqrt(x+3) is x=-2,x=(-3+sqrt(5))/2

Solve for x: (-x-1)^2-3=-1-sqrt(x+3)

The solution is x=-2,x=(-3+sqrt(5))/2

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(- x - 1)^{2} - 3 = - 1 - x + 3

x = - 2, x = \frac{- 3 + 5}{2}

Decimal Notation

x = - 2, x = - 0.38196 \dots

Solution steps

(- x - 1)^{2} - 3 = - 1 - x + 3

Expand

(- x - 1)^{2} - 3 : x^{2} + 2 x - 2

x^{2} + 2 x - 2 = - 1 - x + 3

Remove square roots

x^{4} + 4 x^{3} + 2 x^{2} - 4 x + 1 = x + 3

Solve

x^{4} + 4 x^{3} + 2 x^{2} - 4 x + 1 = x + 3 : x = 1, x = - 2, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

x = 1, x = - 2, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Verify Solutions:

x = 1

False

, x = - 2

True

, x = \frac{- 3 + 5}{2}

True

, x = \frac{- 3 - 5}{2}

False

The solutions are

x = - 2, x = \frac{- 3 + 5}{2}

2 (x - 1)^{\frac{2}{3}} = 32

y, x = 1 + y^{2}

3 x + 8 - 2 x - 4 = 8

x - 2 x - 8 = 8

2 x + 5 = 7

What is the answer to (-x-1)^2-3=-1-sqrt(x+3) ?
The answer to (-x-1)^2-3=-1-sqrt(x+3) is x=-2,x=(-3+sqrt(5))/2
Solve for x: (-x-1)^2-3=-1-sqrt(x+3)
The solution is x=-2,x=(-3+sqrt(5))/2