Trigonometry Examples

$x (x + 1) = 56$

Step 1

Simplify $x (x + 1)$ .

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Step 1.1

Apply the distributive property.

$x \cdot x + x \cdot 1 = 56$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 = 56$

Step 1.2.2

Multiply $x$ by $1$ .

$x^{2} + x = 56$

Step 2

Subtract $56$ from both sides of the equation.

$x^{2} + x - 56 = 0$

Step 3

Factor $x^{2} + x - 56$ 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 $- 56$ and whose sum is $1$ .

$- 7, 8$

Step 3.2

Write the factored form using these integers.

$(x - 7) (x + 8) = 0$

Step 4

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

$x - 7 = 0$

$x + 8 = 0$

Step 5

Set $x - 7$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 5.2

Add $7$ to both sides of the equation.

$x = 7$

Step 6

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

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Step 6.1

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

$x + 8 = 0$

Step 6.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 7

The final solution is all the values that make $(x - 7) (x + 8) = 0$ true.

$x = 7, - 8$