# Solving 11x2+-23x+-13 using the Quadratic Formula

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:
11x2+-23x+-13=0.

There are two real solutions: x = 2.5536963657306, and x = -0.46278727482155.

## Here's how we found that solution:

You entered the following equation:
(1)           11x2+-23x+-13=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)           $$x=--23\pm\frac{\sqrt{-23^2-4*11*-13}}{2*11}$$

which simplifies to:
(4)           $$x=--23\pm\frac{\sqrt{529--572}}{22}$$

Now, solving for x, we find two real solutions:
$$x=\frac{--23+33.181320046074}{22}$$ = 2.5536963657306,
and
$$x=\frac{--23-33.181320046074}{22}$$ = -0.46278727482155,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 11x2+-23x+-13=0.

### Notes

A quadratic equation is any function that has the form: ax2 + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are called coefficients. Also, it should be mentioned that a cannot equal to 0 in the equation ax2+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.