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
Reset

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 equation that can be written as: ax2 + bx + c = 0. In this equation, x is unknown. A, b, and c are constants. A and b are called coefficients. Also, it should be pointed out that a cannot equal to zero in the equation ax2+bx+c=0. If a equals 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 straightforward. Solving a quadratic equation requires more work. Fortunately, you have this handy-dandy quadratic equation calculator. Acutally, quadratic equations can be always 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:


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, these two roots may be equal, resulting in one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to compute answers in many real-world fields, including physics, pharmacokinetics and business.

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 this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. 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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