100x^2 - 20x + 1 = 0: Solving a Quadratic Equation
In this article, we will explore how to solve the quadratic equation 100x^2 - 20x + 1 = 0. This equation is a classic example of a quadratic equation, which is a polynomial equation of degree two.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two. The general form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants, and x is the variable.
Solving the Equation
To solve the equation 100x^2 - 20x + 1 = 0, we can try to factor the left-hand side of the equation. However, in this case, factoring is not possible.
So, we will use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 100, b = -20, and c = 1. Plugging these values into the formula, we get:
x = (20 ± √((-20)^2 - 4(100)(1))) / 2(100)
x = (20 ± √(400 - 400)) / 200
x = (20 ± √0) / 200
x = 20 / 200
x = 1/10
Solutions
So, the solutions to the equation 100x^2 - 20x + 1 = 0 are:
x = 1/10
This means that the value of x that satisfies the equation is 1/10.
Conclusion
In conclusion, we have successfully solved the quadratic equation 100x^2 - 20x + 1 = 0 using the quadratic formula. The solution to the equation is x = 1/10.
