Algebra Examples

$124 = x^{2} + 3$

Step 1

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.1

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

$124 - x^{2} = 3$

Step 1.2

Subtract $3$ from both sides of the equation.

$124 - x^{2} - 3 = 0$

Step 2

Subtract $3$ from $124$ .

$- x^{2} + 121 = 0$

Step 3

Rewrite $121$ as $11^{2}$ .

$- x^{2} + 11^{2} = 0$

Step 4

Reorder $- x^{2}$ and $11^{2}$ .

$11^{2} - x^{2} = 0$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 11$ and $b = x$ .

$(11 + x) (11 - x) = 0$

Step 6

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

$11 + x = 0$

$11 - x = 0$

Step 7

Set $11 + x$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 7.1

Set $11 + x$ equal to $0$ .

$11 + x = 0$

Step 7.2

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 8

Set $11 - x$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 8.1

Set $11 - x$ equal to $0$ .

$11 - x = 0$

Step 8.2

Solve $11 - x = 0$ for $x$ .

Tap for more steps...

Step 8.2.1

Subtract $11$ from both sides of the equation.

$- x = - 11$

Step 8.2.2

Divide each term in $- x = - 11$ by $- 1$ and simplify.

Tap for more steps...

Step 8.2.2.1

Divide each term in $- x = - 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1}$

Step 8.2.2.2

Simplify the left side.

Tap for more steps...

Step 8.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1}$

Step 8.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1}$

Step 8.2.2.3

Simplify the right side.

Tap for more steps...

Step 8.2.2.3.1

Divide $- 11$ by $- 1$ .

$x = 11$

Step 9

The final solution is all the values that make $(11 + x) (11 - x) = 0$ true.

$x = - 11, 11$