Solving 95x2+-59x+8 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:
95x2+-59x+8=0.

There are two real solutions: x = 0.42105263157895, and x = 0.2.

Here's how we found that solution:

You entered the following equation:
(1)           95x2+-59x+8=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)           \(x=--59\pm\frac{\sqrt{-59^2-4*95*8}}{2*95}\)

which simplifies to:
(4)           \(x=--59\pm\frac{\sqrt{3481-3040}}{190}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--59+21}{190}\) = 0.42105263157895,
  and
\(x=\frac{--59-21}{190}\) = 0.2,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 95x2+-59x+8=0.






Notes

What is a quadratic equation? Any function that has the form: ax2 + bx + c = 0. In this equation, x is an unknown, and a, b, and c are constants. The constants a and b are called coefficients. It should be noted that a cannot be 0 in the equation ax2+bx+c=0. If a equals 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.

Solving a linear equation is relatively basic. Solving a quadratic equation requires some more advanced mathematics. Fortunately, you have this handy-dandy quadratic equation solver. Acutally, 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:


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. Depending on the values of a, b, and c, both roots may equal each other, meaning there will only be one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to compute answers in many real-world fields, including physics, pharmacokinetics and architecture.

The term "quadratic" comes from the Latin word quadratum, which means "square." Why? Because what defines a quadratic equation is the inclusion of some variable squared. In our equation above, the term x2 (x squared) is what makes this equation quadratic.

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, 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.

click here for a random example of a quadratic equation.