Precalculus Examples Polynomial and Rational Functions

Solve for x

$\sqrt{x} - 3 = 4$

Step 1

Move all terms not containing $\sqrt{x}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $3$ to both sides of the equation.

$\sqrt{x} = 4 + 3$

Step 1.2

Add $4$ and $3$ .

$\sqrt{x} = 7$

Step 2

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

${\sqrt{x}}^{2} = 7^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

${(x^{\frac{1}{2}})}^{2} = 7^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

Tap for more steps...

Step 3.2.1.1.1

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

$x^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 7^{2}$

Step 3.2.1.2

Simplify.

$x = 7^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise $7$ to the power of $2$ .

$x = 49$

Enter YOUR Problem

Polynomial and Rational Functions

More step-by-step Precalculus examples from this chapter.

How to Use Step-by-Step Examples

Read the worked problem

Each example starts from a real Precalculus problem and shows the rule or formula it relies on.

Follow every step

Work through the solution line by line. Underlined terms open a glossary definition.

Solve your own problem

Enter a similar problem in the Precalculus solver to get the answer with steps.

Why use Mathway?

Step-by-step solutions

See how every answer is worked out, not just the result.

Every major math subject

From basic math through calculus, statistics and chemistry.

Accurate results

Answers you can check your homework against.

Trusted by students

A reliable tool for homework and learning.

Solve for x

Polynomial and Rational Functions

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Precalculus Help