A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

You entered:

There are two real solutions: x = 2.5536963657306, and x = -0.46278727482155.

(1)

For any quadratic equation

(2)

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:

(3) \(x=--23\pm\frac{\sqrt{-23^2-4*11*-13}}{2*11}\)

which simplifies to:

(4) \(x=--23\pm\frac{\sqrt{529--572}}{22}\)

\(x=\frac{--23+33.181320046074}{22}\) = 2.5536963657306,

and

\(x=\frac{--23-33.181320046074}{22}\) = -0.46278727482155,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Solving a linear equation is simple. Solving a quadratic equation is not as straightforward. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. The quadratic formula is:

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Under extraordinary circumstances, the two roots may have the same value, producing one solution for x.

Quadratic equations are more than just mathematical mumbo-jumbo Quadratic equations are needed to compute answers to many real-world problems. For example, to compute whether a braking car can stop fast enough to avoid hitting something would require the use of s quadratic equation.

In our equation, a cannot be zero. However, b can be zero, and so can c.

We hope you find this quadratic equation solver useful. We hope the explanations showing how you can solve the equation yourself are educational and helpful. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

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