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 any equation ax2 + bx + c = 0. In this equation, a, b, and c are constants. X is unknown. A and b are called coefficients. Interestingly, a cannot equal zero in the equation ax2+bx+c=0. If a is 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.

Compared to solving a linear equation, solving a quadratic equation requires a few more steps. However, any quadratic equation can readily be solved using the quadratic formula. Here is the quadratic formula:


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 equal each other, producing one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers in many real-world fields, including physics, biology and architecture.

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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