Pre-Algebra Examples

$x^{2} - 3 x - 54 = (x + 6)$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $x$ from both sides of the equation.

$x^{2} - 3 x - 54 - x = 6$

Step 1.2

Subtract $x$ from $- 3 x$ .

$x^{2} - 4 x - 54 = 6$

Step 2

Subtract $6$ from both sides of the equation.

$x^{2} - 4 x - 54 - 6 = 0$

Step 3

Subtract $6$ from $- 54$ .

$x^{2} - 4 x - 60 = 0$

Step 4

Factor $x^{2} - 4 x - 60$ using the AC method.

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Step 4.1

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 $- 60$ and whose sum is $- 4$ .

$- 10, 6$

Step 4.2

Write the factored form using these integers.

$(x - 10) (x + 6) = 0$

Step 5

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

$x - 10 = 0$

$x + 6 = 0$

Step 6

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 6.2

Add $10$ to both sides of the equation.

$x = 10$

Step 7

Set $x + 6$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Step 7.2

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 8

The final solution is all the values that make $(x - 10) (x + 6) = 0$ true.

$x = 10, - 6$