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
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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

An equation that can be written as bx+c=0 is called a linear equation. It has one unknown, x, and 2 constants, b and c. If this equation were also to include the square of x as an unknown, it would become a quadratic equation. What is a quadratic equation? Any function that can take the form:
ax2 + bx + c = 0,
where x is a variable which is not known. A, b, and c are constants. The constants a and b are called coefficients. Interestingly, a cannot equal 0 in the equation ax2+bx+c=0.

Calculating a solution to a quadratic equation may appear daunting. However, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be reliably solved using the quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. Here is the quadratic formula:


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. Depending on the values of a, b, and c, these two roots may have the same value, meaning there will only be one solution for x.

Quadratic equations are an important part of mathematics. 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.

The quadratic equation calculator on this website uses the quadratic formula to solve your quadratic equations, and this is a reliable and relatively simple way to do it. But there are other ways to solve a quadratic equation, such as completing the square or factoring.

We hope you find this quadratic equation solver 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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