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
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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

What is a quadratic equation? Any equation
ax2 + bx + c = 0,
where x is unknown, and a, b, and c are constants. A and b are referred to as coefficients. Further, a cannot equal to zero. 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 quadratic equation can appear challenging. Fortunately, any quadratic equation can reliably be solved using the quadratic formula. 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, both roots may be the same, 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. The laws of motion is one example of an application of quadratic equations.

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

We hope you find this quadratic equation calculator 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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