Quickly Solve a Quadratic Equation

What is a quadratic equation?

A quadratic equation is a mathematical equation that contains a term of degree 2. It has the form ax^2 + bx + c = 0. To solve this type of equation, you can use the quadratic formula. It is also called a second-degree equation.

How the quadratic equation is written

A quadratic equation is written in the form ax^2 + bx + c = 0 (corresponding to ax² + bx + c = 0). The coefficients a, b and c are real numbers. To solve this type of equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.

Other ways of writing the equation

Examples:

• ax² + bx + c = 0
• ax² + bx = -c
• ax² = -bx - c
• x² = (-b/a)x - c/a
• ...

Solving

With this tool, solving a quadratic equation is very easy. You just need to type the data correctly into the field. Then, automatically, the result — that is, the solution or solutions — will be displayed.

Several types of results are possible

For quadratic equations, three types of result are possible.

No real solution

Sometimes a quadratic equation cannot be solved within the real numbers. In that case, a complex solution is offered. For example: x^2+4x=-10.

A single solution

A quadratic equation may have only one solution. For example: x^2=-4+4x.

Two solutions

A quadratic equation can have two distinct solutions. For example, consider the equation: x^2-5x=-6.

Using fractions

You can use fractions in your equation in the "a/b" or "-a/b" formats, but not in the "a/-b" format.

The program converts the fractions to decimal numbers. If a fraction produces a number with infinitely many decimal places, the program provides the result as an approximation. In that case, the solution or solutions are rounded and presented in an approximate form.

Delete everything

If you want to delete everything, just click the Clear button.

Save

If you want to save, just click the Save button.

Export the table

You can also export your results in PDF or CSV format.

How are quadratic equations useful in everyday life?

Quadratic equations are very useful in everyday life. They make it possible to solve concrete problems. For example, they are used to determine the trajectory of a moving object, to calculate the distance between two points, to determine the shape of an object, and so on.

Quadratic equations are also used in physics, chemistry, biology, economics, computer science, etc.

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