Solving 80x2+-28x+-86 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:
80x2+-28x+-86=0.

There are two real solutions: x = 1.2264870422407, and x = -0.87648704224065.

Here's how we found that solution:

You entered the following equation:
(1)           80x2+-28x+-86=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)           \(x=--28\pm\frac{\sqrt{-28^2-4*80*-86}}{2*80}\)

which simplifies to:
(4)           \(x=--28\pm\frac{\sqrt{784--27520}}{160}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--28+168.2379267585}{160}\) = 1.2264870422407,
  and
\(x=\frac{--28-168.2379267585}{160}\) = -0.87648704224065,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 80x2+-28x+-86=0.






Notes

A quadratic equation is an function that has the form: ax2 + bx + c = 0, where x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. It should be noted that a cannot equal 0.

In contrast to solving a linear equation, solving a quadratic equation is a more complicated task. 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 written:


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. Depending on the values of a, b, and c, both roots may be the same, producing one solution for x.

Quadratic equations are important. Quadratic equations are needed to calculate answers to many real-world problems. The distance before a vehicle can stop once you hit the brakes is one example of an application of quadratic equations.

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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