Solving 97x2+44x+-58 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:
97x2+44x+-58=0.

There are two real solutions: x = 0.57903596890156, and x = -1.0326442163242.

Here's how we found that solution:

You entered the following equation:
(1)           97x2+44x+-58=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)           \(x=-44\pm\frac{\sqrt{44^2-4*97*-58}}{2*97}\)

which simplifies to:
(4)           \(x=-44\pm\frac{\sqrt{1936--22504}}{194}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-44+156.3329779669}{194}\) = 0.57903596890156,
  and
\(x=\frac{-44-156.3329779669}{194}\) = -1.0326442163242,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 97x2+44x+-58=0.






Notes

What is a quadratic equation? Any function that can take the form: ax2 + bx + c = 0. In this equation, x is an unknown, and a, b, and c are constants. The constants a and b are called coefficients. It should be pointed out that a cannot equal to 0. If a is equal to 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.

In contrast to solving a linear equation, solving a quadratic equation requires a few more steps. 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. Under extraordinary circumstances, both roots may equal each other, producing one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to compute 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 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 encourage you to plug in different values for a, b, and c. 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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