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 equation that can take 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. Furthermore, it is worth pointing out that a cannot be zero.

Solving a linear equation is fairly simple. Solving a quadratic equation requires more work. Fortunately, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be quickly solved using the quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. The quadratic formula is:


Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Rarely, the two roots may equal each other, producing one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to calculate answers to many real-world problems. For example, to compute how an object will rise and fall due to Earth's gravity 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 hope you find this quadratic equation solver useful. 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 Quadratic-Equation-Calculator.com.

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