Pre-Algebra Examples

$17 x + x^{2} = - 52$

Step 1

Add $52$ to both sides of the equation.

$17 x + x^{2} + 52 = 0$

Step 2

Factor the left side of the equation.

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Step 2.1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$17 u + u^{2} + 52 = 0$

Step 2.2

Factor $17 u + u^{2} + 52$ using the AC method.

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Step 2.2.1

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 $52$ and whose sum is $17$ .

$4, 13$

Step 2.2.2

Write the factored form using these integers.

$(u + 4) (u + 13) = 0$

Step 2.3

Replace all occurrences of $u$ with $x$ .

$(x + 4) (x + 13) = 0$

Step 3

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

$x + 4 = 0$

$x + 13 = 0$

Step 4

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 4.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 5

Set $x + 13$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x + 13$ equal to $0$ .

$x + 13 = 0$

Step 5.2

Subtract $13$ from both sides of the equation.

$x = - 13$

Step 6

The final solution is all the values that make $(x + 4) (x + 13) = 0$ true.

$x = - 4, - 13$