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

A quadratic equation is an function that can be written in the form:
ax2 + bx + c = 0.
\ In this equation, x is unknown. A, b, and c are constants. The constants a and b, are referred to as coefficients. Further, it should be noted that a cannot be zero in the equation ax2+bx+c=0.

Calculating a solution to a quadratic equation can appear daunting. Fortunately, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be quickly solved using the quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. The quadratic formula is written:


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. Under extraordinary circumstances, the two roots may be the same, producing one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers to many real-world problems. The distance before a vehicle can stop once you hit the brakes is one example of an application of quadratic equations.

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 hope you find this quadratic equation solver useful. 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 your interest in Quadratic-Equation-Calculator.com.

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