Free Algebra
Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

Math solver on your site

Please use this form if you would like
to have this math solver on your website,
free of charge.

Name:

Email:

Your Website:

Msg:

Solving Quadratic Equations Using the Quadratic Formula

Example

Solve using the quadratic formula: 36x² + 16 + 48x = 0

Solution

Step 1 Write the quadratic equation in standard form, ax² + bx + c = 0.	36x² + 16 + 48x = 0
On the left side, write the terms in decreasing powers of x. Each term is divisible by 4. To simplify the calculations, divide both sides of the equation by 4. Step 2 Identify the values of a, b, and c.	36x² + 16 + 48x = 0
Step 3 Substitute the values of a, b, and c into the quadratic formula.
Step 4 Simplify.
Step 5 Check each solution. We leave the check to you.

We say that is a solution of multiplicity two.

Example 2

Solve using the quadratic formula: x² + 5 = 3x

Step 1 Write the quadratic equation in standard form, ax² + bx + c = 0.	x² + 5 = 3x
Subtract 3x from both sides of the equation. Step 2 Identify the values of a, b, and c.
Step 3 Substitute the values of a, b, and c into the quadratic formula.
Step 4 Simplify.

Notice the negative number under the square root symbol.

The radical does not represent a real number.

Therefore, the equation x² + 5 = 3x has no real number solutions.