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
Reset

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 function that has the form: ax2 + bx + c = 0. In this equation, x is an unknown, and a, b, and c are constants. A and b are referred to as coefficients. Further, a cannot equal to zero in the equation ax2+bx+c=0. If a=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.

Solving a linear equation is relatively basic. Solving a quadratic equation requires some more advanced mathematics. 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 written:


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 equal each other, meaning there will only be one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to compute answers in many real-world fields, including physics, pharmacokinetics and architecture.

In our equation, a cannot be zero. However, b can be zero, and so can c.

We this quadratic equation calculator is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. 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.

click here for a random example of a quadratic equation.