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

You entered:

There are two real solutions: x = 1.2264870422407, and x = -0.87648704224065.

(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) \(x=--28\pm\frac{\sqrt{-28^2-4*80*-86}}{2*80}\)

which simplifies to:

(4) \(x=--28\pm\frac{\sqrt{784--27520}}{160}\)

\(x=\frac{--28+168.2379267585}{160}\) = 1.2264870422407,

and

\(x=\frac{--28-168.2379267585}{160}\) = -0.87648704224065,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

where x is unknown. A, b, and c are constants. A and b are referred to as coefficients. It is worth noting that a cannot equal 0 in the equation ax

In contrast to solving a linear equation, solving a quadratic equation requires a few more steps. Fortunately, any quadratic equation can always be solved using the quadratic formula. The quadratic formula is written:

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, the two roots may equal each other, producing one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to compute answers to many real-world problems. For example, to compute the path of an accelerating object 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 calculator useful. 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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