Algebra Examples

$f (x) = - \sqrt{5 x + 2} - 1$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \sqrt{5 x + 2} - 1$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $- \sqrt{5 x + 2} - 1 = 0$ .

$- \sqrt{5 x + 2} - 1 = 0$

Step 1.2.2

Add $1$ to both sides of the equation.

$- \sqrt{5 x + 2} = 1$

Step 1.2.3

To remove the radical on the left side of the equation, square both sides of the equation.

${(- \sqrt{5 x + 2})}^{2} = 1^{2}$

Step 1.2.4

Simplify each side of the equation.

Tap for more steps...

Step 1.2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x + 2}$ as ${(5 x + 2)}^{\frac{1}{2}}$ .

${(- {(5 x + 2)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 1.2.4.2

Simplify the left side.

Tap for more steps...

Step 1.2.4.2.1

Simplify ${(- {(5 x + 2)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 1.2.4.2.1.1

Apply the product rule to $- {(5 x + 2)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(5 x + 2)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 1.2.4.2.1.2

Raise $- 1$ to the power of $2$ .

$1 {({(5 x + 2)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 1.2.4.2.1.3

Multiply ${({(5 x + 2)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(5 x + 2)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 1.2.4.2.1.4

Multiply the exponents in ${({(5 x + 2)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 1.2.4.2.1.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(5 x + 2)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 1.2.4.2.1.4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.4.2.1.4.2.1

Cancel the common factor.

${(5 x + 2)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 1.2.4.2.1.4.2.2

Rewrite the expression.

${(5 x + 2)}^{1} = 1^{2}$

Step 1.2.4.2.1.5

Simplify.

$5 x + 2 = 1^{2}$

Step 1.2.4.3

Simplify the right side.

Tap for more steps...

Step 1.2.4.3.1

One to any power is one.

$5 x + 2 = 1$

Step 1.2.5

Solve for $x$ .

Tap for more steps...

Step 1.2.5.1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 1.2.5.1.1

Subtract $2$ from both sides of the equation.

$5 x = 1 - 2$

Step 1.2.5.1.2

Subtract $2$ from $1$ .

$5 x = - 1$

Step 1.2.5.2

Divide each term in $5 x = - 1$ by $5$ and simplify.

Tap for more steps...

Step 1.2.5.2.1

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 1.2.5.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.5.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.2.5.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 1.2.5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Step 1.2.5.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.5.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 1.2.6

Exclude the solutions that do not make $0 = - \sqrt{5 x + 2} - 1$ true.

$No solution$

Step 1.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \sqrt{5 (0) + 2} - 1$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $5$ by $0$ .

$y = - \sqrt{0 + 2} - 1$

Step 2.2.2

Add $0$ and $2$ .

$y = - \sqrt{2} - 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \sqrt{2} - 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \sqrt{2} - 1)$

Step 4