Solving 27x2+-94x+73 using the Quadratic Formula

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


For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

a
 
x2
 
+
b
 
x
 
+
c
 
= 0
Reset

You entered:
27x2+-94x+73=0.

There are two real solutions: x = 2.3121203192793, and x = 1.1693611622022.

Here's how we found that solution:

You entered the following equation:
(1)           27x2+-94x+73=0.

For any quadratic equation ax2 + bx + c = 0, one can solve for x using the following equation, which is known as the quadratic formula:
(2)          

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:
(3)           \(x=--94\pm\frac{\sqrt{-94^2-4*27*73}}{2*27}\)

which simplifies to:
(4)           \(x=--94\pm\frac{\sqrt{8836-7884}}{54}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--94+30.854497241083}{54}\) = 2.3121203192793,
  and
\(x=\frac{--94-30.854497241083}{54}\) = 1.1693611622022,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 27x2+-94x+73=0.






Notes

A quadratic equation is any function that takes the form: ax2 + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are called coefficients. Interestingly, a cannot be zero in the equation ax2+bx+c=0. If a=0, then ax2=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Calculating a solution to a quadratic equation can be intimidating. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be reliably solved using the quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. This 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. Rarely, these two roots may equal each other, resulting in one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to find answers to many real-world problems. The contour of a parablolic dish antenna is one example of an application of quadratic equations.

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 encourage you to try it with different values, and to read the explanation for how to reach your answer. 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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