Algebra Examples

$g (- x) = x^{2}$

Step 1

Rewrite using the commutative property of multiplication.

$- g x = x^{2}$

Step 2

Subtract $x^{2}$ from both sides of the equation.

$- g x - x^{2} = 0$

Step 3

Factor $x$ out of $- g x - x^{2}$ .

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Step 3.1

Factor $x$ out of $- g x$ .

$x (- g) - x^{2} = 0$

Step 3.2

Factor $x$ out of $- x^{2}$ .

$x (- g) + x (- x) = 0$

Step 3.3

Factor $x$ out of $x (- g) + x (- x)$ .

$x (- g - x) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$- g - x = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $- g - x$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $- g - x$ equal to $0$ .

$- g - x = 0$

Step 6.2

Solve $- g - x = 0$ for $x$ .

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Step 6.2.1

Add $g$ to both sides of the equation.

$- x = g$

Step 6.2.2

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

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Step 6.2.2.1

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

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

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Dividing two negative values results in a positive value.

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

Step 6.2.2.2.2

Divide $x$ by $1$ .

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

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Move the negative one from the denominator of $\frac{g}{- 1}$ .

$x = - 1 \cdot g$

Step 6.2.2.3.2

Rewrite $- 1 \cdot g$ as $- g$ .

$x = - g$

Step 7

The final solution is all the values that make $x (- g - x) = 0$ true.

$x = 0$

$x = - g$