Solving 11x2+49x+15 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:
11x2+49x+15=0.

There are two real solutions: x = -0.33066854136136, and x = -4.1238769131841.

Here's how we found that solution:

You entered the following equation:
(1)           11x2+49x+15=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)           \(x=-49\pm\frac{\sqrt{49^2-4*11*15}}{2*11}\)

which simplifies to:
(4)           \(x=-49\pm\frac{\sqrt{2401-660}}{22}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-49+41.72529209005}{22}\) = -0.33066854136136,
  and
\(x=\frac{-49-41.72529209005}{22}\) = -4.1238769131841,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 11x2+49x+15=0.






Notes

What is a quadratic equation? Any equation that takes the form:
ax2 + bx + c = 0.
\ In this equation, x is a variable which is not known, and a, b, and c are constants. The constants a and b are called coefficients. It should be pointed out that a cannot be zero in the equation ax2+bx+c=0.

Solving a linear equation is simple. Solving a quadratic equation is not quite so straightforward. Fortunately, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be reliably 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:


When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Rarely, both roots may have the same value, resulting in one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to find answers to many real-world problems. For example, to compute the path of an accelerating object would require the use of s quadratic equation.

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 try it with different values, and to read the explanation for how to reach your answer. 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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