Solving 65x2+-13x+-63 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:
65x2+-13x+-63=0.

There are two real solutions: x = 1.0895608971816, and x = -0.88956089718156.

Here's how we found that solution:

You entered the following equation:
(1)           65x2+-13x+-63=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)           \(x=--13\pm\frac{\sqrt{-13^2-4*65*-63}}{2*65}\)

which simplifies to:
(4)           \(x=--13\pm\frac{\sqrt{169--16380}}{130}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--13+128.6429166336}{130}\) = 1.0895608971816,
  and
\(x=\frac{--13-128.6429166336}{130}\) = -0.88956089718156,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 65x2+-13x+-63=0.






Notes

A quadratic equation is any equation that has the form: ax2 + bx + c = 0, where a, b, and c are constants. X is an unknown. A and b are called coefficients. Interestingly, a cannot equal to 0 in the equation ax2+bx+c=0.

Solving a linear equation is basic. Solving a quadratic equation is not as simple. Fortunately, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be quickly 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:


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, 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 calculate the path of an accelerating object would require the use of s quadratic equation.

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.

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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