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
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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 an equation
ax2 + bx + c = 0.
\ In this equation, x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. Further, it is worth noting that a cannot equal to 0.

Finding a solution to a quadratic equation can appear daunting. However, there are a number of methods for solving quadratic equations. One of the most widely used is 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. Depending on the values of a, b, and c, these two roots may have the same value, producing one solution for x.

Quadratic equations are important. Quadratic equations are needed to find answers to many real-world problems. For example, to calculate the path of an accelerating object would require the use of s quadratic equation.

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 hope the explanations showing how you can solve the equation yourself are educational and helpful. 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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