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

You entered:

There are two real solutions: x = 0.62422813026934, and x = -1.6242281302693.

(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) \(x=-72\pm\frac{\sqrt{72^2-4*72*-73}}{2*72}\)

which simplifies to:

(4) \(x=-72\pm\frac{\sqrt{5184--21024}}{144}\)

\(x=\frac{-72+161.88885075878}{144}\) = 0.62422813026934,

and

\(x=\frac{-72-161.88885075878}{144}\) = -1.6242281302693,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

where x is a variable which is not known. A, b, and c are constants. The constants a and b are called coefficients. It should be mentioned that a cannot be equal to zero. If a equals 0, then ax

In contrast to solving a linear equation, solving a quadratic equation is a more complicated task. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. Here is the quadratic formula:

When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Under extraordinary circumstances, these two roots may have the same value, producing one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate 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.

The term "quadratic" comes from the Latin word

We this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

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