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

What is a quadratic equation? A quadratic equation is an function that can be written as:
ax2 + bx + c = 0.
\ In this equation, a, b, and c are constants. X is an unknown. A and b are called coefficients. It should be mentioned that a cannot be zero in the equation ax2+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is basic. Solving a quadratic equation is more complex. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be readily solved using the quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. The quadratic formula is written:


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, producing one solution for x.

Quadratic equations are 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.

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, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

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