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,
where a, b, and c are constants. X is unknown. A and b are referred to as coefficients. It is worth mentioning that a cannot be 0 in the equation ax2+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a quadratic equation may appear daunting, because both x and x2 are unknown. However, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be readily 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. This 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 be the same, meaning there will only be one solution for x.

Quadratic equations are more than just mathematical mumbo-jumbo Quadratic equations are needed to calculate answers in many real-world fields, including engineering, pharmacokinetics and business.

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 this quadratic equation solver is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.

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