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

A quadratic equation is any equation that can be written as: ax2 + bx + c = 0. In this equation, x is a variable of unknown value. A, b, and c are constants. A and b are called coefficients. Interestingly, a cannot be equal to 0.

Calculating a solution to a quadratic equation can seem challenging. However, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be quickly 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 calculate answers to many real-world problems. The contour of a parablolic mirror is one example of an application of quadratic equations.

As mentioned above, in the equation ax2+bx+c=0, a cannot be zero. If a were 0, then ax2 = 0x2 = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

We this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. 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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