Algebra Examples

$x^{2} + 6 x + 5 = 0$

Step 1

Factor $x^{2} + 6 x + 5$ using the AC method.

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Step 1.1

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 $5$ and whose sum is $6$ .

$1, 5$

Step 1.2

Write the factored form using these integers.

$(x + 1) (x + 5) = 0$

Step 2

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

$x + 1 = 0$

$x + 5 = 0$

Step 3

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 3.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 4

Set $x + 5$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Step 4.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 5

The final solution is all the values that make $(x + 1) (x + 5) = 0$ true.

$x = - 1, - 5$