help with this algebra problem?!!?

-2(√x) = -1 – x =>

4x = x^2 + 2x + 1 (after squaring both sides of equation) =>

0 = x^2 – 2x + 1 (after subtracting 4x from both sides of equation) =>

0 = (x – 1)^2 = (x – 1)(x – 1) (after factoring the right-side polynomial) =>

0 = x – 1 or 0 = x – 1 (identification of roots, or, in this case, a single double-root) =>

>>> 1 = x <<< (simple algebraic solving, disregarding repeated root)

1. Sqaure both sides

(-2√x)^2 = (-1-x)(-1-x)

4x = x^2+2x+1

2. Set the equation equal to zero (subtract 4x from each side)

0 = x^2-2x+1 (ax^2+bx+c)

3. Now you can use the quadratic formula,

(-b +/- √(b^2 – 4ac)) ÷ 2a,

and plug in the values from your quadratic equation,

(2 +/- √(-2^2 – (4)(1)(1))) ÷ 2(1),

which equals (2 +/- √0) ÷ 2.

4. More simplifying leaves you with 2 ÷ 2, or 1. So, x=1. If you plug 1 in as the value for x in your original equation, it works.

The source web site does a good job of explaining the quadratic formula and has examples, might be helpful to you. Hope I helped. 🙂

-2√x = -1-x

2√x = 1 + x (multiply by -1 on both sides)

4x^2 = (1 + x)^2 (sqaure both sides)

4x^2 = x^2 + 2x + 1 (extend)

3x^2 -2x -1 = 0 (Move all into one side)

(3x + 1) (x – 1) = 0 (factorise)

x = -1/3

OR

x = 1

Since x in √x cannot be negative, the only accepted answer would be x = 1

I tried to do it in my mind, but im in summer mode. Go to the link below and they have a “universal simplifier and solver”. Hope It Helps!