Solve for x 2(x-1)^2-2x^2=4

$2 {(x - 1)}^{2} - 2 x^{2} = 4$

Subtract $4$ from both sides of the equation.

$2 {(x - 1)}^{2} - 2 x^{2} - 4 = 0$

Simplify $2 {(x - 1)}^{2} - 2 x^{2} - 4$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$2 ((x - 1) (x - 1)) - 2 x^{2} - 4 = 0$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$2 (x (x - 1) - 1 (x - 1)) - 2 x^{2} - 4 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 2 x^{2} - 4 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 2 x^{2} - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 2 x^{2} - 4 = 0$

Move $- 1$ to the left of $x$ .

$2 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 2 x^{2} - 4 = 0$

Rewrite $- 1 x$ as $- x$ .

$2 (x^{2} - x - 1 x - 1 \cdot - 1) - 2 x^{2} - 4 = 0$

Rewrite $- 1 x$ as $- x$ .

$2 (x^{2} - x - x - 1 \cdot - 1) - 2 x^{2} - 4 = 0$

Multiply $- 1$ by $- 1$ .

$2 (x^{2} - x - x + 1) - 2 x^{2} - 4 = 0$

Subtract $x$ from $- x$ .

$2 (x^{2} - 2 x + 1) - 2 x^{2} - 4 = 0$

Apply the distributive property.

$2 x^{2} + 2 (- 2 x) + 2 \cdot 1 - 2 x^{2} - 4 = 0$

Simplify.

Multiply $- 2$ by $2$ .

$2 x^{2} - 4 x + 2 \cdot 1 - 2 x^{2} - 4 = 0$

Multiply $2$ by $1$ .

$2 x^{2} - 4 x + 2 - 2 x^{2} - 4 = 0$

Combine the opposite terms in $2 x^{2} - 4 x + 2 - 2 x^{2} - 4$ .

Subtract $2 x^{2}$ from $2 x^{2}$ .

$- 4 x + 2 + 0 - 4 = 0$

Add $- 4 x + 2$ and $0$ .

$- 4 x + 2 - 4 = 0$

Subtract $4$ from $2$ .

$- 4 x - 2 = 0$

Factor $- 2$ out of $- 4 x - 2$ .

Factor $- 2$ out of $- 4 x$ .

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

Factor $- 2$ out of $- 2$ .

$- 2 (2 x) - 2 \cdot 1 = 0$

Factor $- 2$ out of $- 2 (2 x) - 2 (1)$ .

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

Divide each term in $- 2 (2 x + 1) = 0$ by $- 2$ and simplify.

Divide each term in $- 2 (2 x + 1) = 0$ by $- 2$ .

$\frac{- 2 (2 x + 1)}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (2 x + 1)}{- 2} = \frac{0}{- 2}$

Divide $2 x + 1$ by $1$ .

$2 x + 1 = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$2 x + 1 = 0$

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$

Solve for x 2(x-1)^2-2x^2=4

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