Solving 22x2+98x+96 using the Quadratic Formula

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 any equation that has the form:
ax2 + bx + c = 0.
\ In this equation, x is unknown, and a, b, and c are constants. The constants a and b are called coefficients. Also, it is worth noting that a cannot equal zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Compared to solving a linear equation, solving a quadratic equation requires a few more steps. However, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be always 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. The quadratic formula is:

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, meaning there will only be one solution for x.

Why do we need to be able to solve quadratic equations? 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.

We hope you find this quadratic equation calculator useful. 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.