Pre-Algebra Examples

$x^{2} = 24 - 10 x$

Step 1

Add $10 x$ to both sides of the equation.

$x^{2} + 10 x = 24$

Step 2

Subtract $24$ from both sides of the equation.

$x^{2} + 10 x - 24 = 0$

Step 3

Factor $x^{2} + 10 x - 24$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $10$ .

$- 2, 12$

Step 3.2

Write the factored form using these integers.

$(x - 2) (x + 12) = 0$

Step 4

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

$x - 2 = 0$

$x + 12 = 0$

Step 5

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$x = 2$

Step 6

Set $x + 12$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Step 6.2

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 7

The final solution is all the values that make $(x - 2) (x + 12) = 0$ true.

$x = 2, - 12$