Solving 66x2+-66x+-77 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:
66x2+-66x+-77=0.

There are two real solutions: x = 1.6902380714238, and x = -0.69023807142381.

Here's how we found that solution:

You entered the following equation:
(1)           66x2+-66x+-77=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)           \(x=--66\pm\frac{\sqrt{-66^2-4*66*-77}}{2*66}\)

which simplifies to:
(4)           \(x=--66\pm\frac{\sqrt{4356--20328}}{132}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--66+157.11142542794}{132}\) = 1.6902380714238,
  and
\(x=\frac{--66-157.11142542794}{132}\) = -0.69023807142381,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 66x2+-66x+-77=0.






Notes

A quadratic equation is an function that can be written in the form:
ax2 + bx + c = 0.
\ In this equation, x is a variable of unknown value. A, b, and c are constants. The constants a and b, are referred to as coefficients. Also, it is worth noting that a cannot be equal to zero. If a is equal to 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.

Calculating a solution to a quadratic equation may appear daunting. Fortunately, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. The quadratic formula is:


Solving a quadratic equation will always result in 2 solutions for x. These solutions are 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, the two roots may have the same value, meaning there will only be one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to compute answers to many real-world problems. The acceleration of an object as it falls to earth 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 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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