Solving 72x2+72x+-73 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:
72x2+72x+-73=0.

There are two real solutions: x = 0.62422813026934, and x = -1.6242281302693.

Here's how we found that solution:

You entered the following equation:
(1)           72x2+72x+-73=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)           \(x=-72\pm\frac{\sqrt{72^2-4*72*-73}}{2*72}\)

which simplifies to:
(4)           \(x=-72\pm\frac{\sqrt{5184--21024}}{144}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-72+161.88885075878}{144}\) = 0.62422813026934,
  and
\(x=\frac{-72-161.88885075878}{144}\) = -1.6242281302693,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 72x2+72x+-73=0.






Notes

A quadratic equation is an function that can be written as: ax2 + bx + c = 0. In this equation, x is a variable which is not known, and a, b, and c are constants. The constants a and b are called coefficients. It should be mentioned that a cannot be 0.

Solving a linear equation is straightforward. Solving a quadratic equation is less so. 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. Under extraordinary circumstances, both roots may be equal, resulting in one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to compute answers to many real-world problems. For example, to compute the path of an accelerating object would require the use of s quadratic equation.

The quadratic formula has been known for centuries. Brahmagupta, a mathematician from India, first described the quadratic formula as a means to calculate solutions to quadratic equations in the 7th Century AD.

We this quadratic equation solver is useful to you. We encourage you to plug in different values for a, b, and c. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.

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