Solving 22x2+98x+96 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:
22x2+98x+96=0.

There are two real solutions: x = -1.4545454545455, and x = -3.

Here's how we found that solution:

You entered the following equation:
(1)           22x2+98x+96=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)           \(x=-98\pm\frac{\sqrt{98^2-4*22*96}}{2*22}\)

which simplifies to:
(4)           \(x=-98\pm\frac{\sqrt{9604-8448}}{44}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-98+34}{44}\) = -1.4545454545455,
  and
\(x=\frac{-98-34}{44}\) = -3,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 22x2+98x+96=0.






Notes

A quadratic equation is any equation that has the form:
ax2 + bx + c = 0,
where x is an unknown, and a, b, and c are constants. A and b are referred to as coefficients. Also, a cannot be equal to 0 in the equation ax2+bx+c=0. If a is 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.

Calculating a solution to a quadratic equation may appear daunting, because both x and x2 are unknown. However, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. 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 be the same, producing one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to calculate answers in many real-world fields, including engineering, pharmacokinetics and business.

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 this quadratic equation solver is useful to you. 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 using Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.