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

You entered:

There are two real solutions: x = 1.6902380714238, and x = -0.69023807142381.

(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) \(x=--66\pm\frac{\sqrt{-66^2-4*66*-77}}{2*66}\)

which simplifies to:

(4) \(x=--66\pm\frac{\sqrt{4356--20328}}{132}\)

\(x=\frac{--66+157.11142542794}{132}\) = 1.6902380714238,

and

\(x=\frac{--66-157.11142542794}{132}\) = -0.69023807142381,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

\ In this equation, x is a variable which is not known, and a, b, and c are constants. A and b are referred to as coefficients. Interestingly, a cannot equal to zero. If a is 0, then ax

Calculating a solution to a quadratic equation may appear daunting, because both x and x

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, both roots may be the same, meaning there will only be one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to find answers to many real-world problems. The geometry of a parablolic dish antenna is one example of an application of quadratic equations.

The term "quadratic" comes from the Latin word

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