Trigonometry Examples

$\sqrt{4 x + 76} = 2 x - 2$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$\sqrt{4 x + 76} - 2 x = - 2$

Step 1.2

Add $2$ to both sides of the equation.

$\sqrt{4 x + 76} - 2 x + 2 = 0$

Step 2

Simplify each term.

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Step 2.1

Factor $4$ out of $4 x + 76$ .

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Step 2.1.1

Factor $4$ out of $4 x$ .

$\sqrt{4 (x) + 76} - 2 x + 2 = 0$

Step 2.1.2

Factor $4$ out of $76$ .

$\sqrt{4 x + 4 \cdot 19} - 2 x + 2 = 0$

Step 2.1.3

Factor $4$ out of $4 x + 4 \cdot 19$ .

$\sqrt{4 (x + 19)} - 2 x + 2 = 0$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} (x + 19)} - 2 x + 2 = 0$

Step 2.3

Pull terms out from under the radical.

$2 \sqrt{x + 19} - 2 x + 2 = 0$

Step 3

Set the radicand in $\sqrt{x + 19}$ less than $0$ to find where the expression is undefined.

$x + 19 < 0$

Step 4

Subtract $19$ from both sides of the inequality.

$x < - 19$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x < - 19$

$(- \infty, - 19)$

Step 6