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 equation that can take the form: ax2 + bx + c = 0, where x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. Further, it is worth mentioning that a cannot be equal to 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.

Solving a linear equation is straightforward. Solving a quadratic equation is less straightforward. However, any quadratic equation can quickly be solved using the quadratic formula. 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. Rarely, the two roots may have the same value, producing one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to compute answers to many real-world problems. The contour of a parablolic dish antenna is one example of an application of quadratic equations.

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.

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