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

A quadratic equation is any equation that has the form:
ax2 + bx + c = 0.
\ In this equation, a, b, and c are constants. X is unknown. A and b are referred to as coefficients. Further, a cannot equal to 0 in the equation ax2+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is pretty straightforward. Solving a quadratic equation requires more work. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. The quadratic formula is:


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. Under extraordinary circumstances, the two roots may have the same value, meaning there will only be one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate answers to many real-world problems. For example, to compute 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.

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