Algebra Examples

$f (x) = - 16 (x^{2} - 7 x - 8)$

Step 1

Set $- 16 (x^{2} - 7 x - 8)$ equal to $0$ .

$- 16 (x^{2} - 7 x - 8) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $- 16 (x^{2} - 7 x - 8) = 0$ by $- 16$ and simplify.

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Step 2.1.1

Divide each term in $- 16 (x^{2} - 7 x - 8) = 0$ by $- 16$ .

$\frac{- 16 (x^{2} - 7 x - 8)}{- 16} = \frac{0}{- 16}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $- 16$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{- 16 (x^{2} - 7 x - 8)}{- 16} = \frac{0}{- 16}$

Step 2.1.2.1.2

Divide $x^{2} - 7 x - 8$ by $1$ .

$x^{2} - 7 x - 8 = \frac{0}{- 16}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $- 16$ .

$x^{2} - 7 x - 8 = 0$

Step 2.2

Factor $x^{2} - 7 x - 8$ 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 $- 8$ and whose sum is $- 7$ .

$- 8, 1$

Step 2.2.2

Write the factored form using these integers.

$(x - 8) (x + 1) = 0$

Step 2.3

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

$x - 8 = 0$

$x + 1 = 0$

Step 2.4

Set $x - 8$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Step 2.4.2

Add $8$ to both sides of the equation.

$x = 8$

Step 2.5

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

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Step 2.5.1

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

$x + 1 = 0$

Step 2.5.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.6

The final solution is all the values that make $(x - 8) (x + 1) = 0$ true.

$x = 8, - 1$

Step 3