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:

= 0

You entered:

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:

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,
\(x=\frac{-44-156.3329779669}{194}\) = -1.0326442163242,

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


What is a quadratic equation? A quadratic equation is any function that has the form:
ax2 + bx + c = 0,
where x is a variable which is not known, and a, b, and c are constants. The constants a and b are called coefficients. Additionally, it is worth noting that a cannot be equal to zero. 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.

In contrast to solving a linear equation, solving a quadratic equation requires a few more steps. However, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be reliably 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. Under extraordinary circumstances, the two roots may have the same value, producing one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to calculate answers to many real-world problems. The contour of a parablolic mirror is one example of an application of quadratic equations.

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 try it with different values, and to read the explanation for how to reach your answer. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for using

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