Trigonometry Examples

$8 x - 4 = x^{2} + 5 x - 14$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + 5 x - 14 = 8 x - 4$

Step 2

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

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Step 2.1

Subtract $8 x$ from both sides of the equation.

$x^{2} + 5 x - 14 - 8 x = - 4$

Step 2.2

Subtract $8 x$ from $5 x$ .

$x^{2} - 3 x - 14 = - 4$

Step 3

Add $4$ to both sides of the equation.

$x^{2} - 3 x - 14 + 4 = 0$

Step 4

Add $- 14$ and $4$ .

$x^{2} - 3 x - 10 = 0$

Step 5

Factor $x^{2} - 3 x - 10$ using the AC method.

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Step 5.1

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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Step 5.2

Write the factored form using these integers.

$(x - 5) (x + 2) = 0$

Step 6

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

$x - 5 = 0$

$x + 2 = 0$

Step 7

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

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Step 7.1

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

$x - 5 = 0$

Step 7.2

Add $5$ to both sides of the equation.

$x = 5$

Step 8

Set $x + 2$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 8.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 9

The final solution is all the values that make $(x - 5) (x + 2) = 0$ true.

$x = 5, - 2$