### Quadratic Equation

Welcome visitors, On this occasion will be discussed about the material quadratic equations. Quadratic equations are equations with the general form: $$ax^2+bx+c=0$$ where $a, b, c$ are real numbers and $a$ are not zero. The coefficient $x^2$ is called the initial value, the coefficient $x$ is called the middle value and the constant is called the final value.

The way to solve this is by factoring and using the abc formula.

**Example 1:**

Find the square root of $x^2+3x+2=0$.

Answer:

We use the factoring method, in this factoring method the initial value must be 1, if not 1 then the final value becomes $ac$ and the initial value becomes 1, then find 2 numbers whose product is the final value and the result is the middle value, after getting two that number then divide by the value $a$. So that we get: $$(x+1)(x+2)=0$$ $x=-1$ and $x=-2$.

**Example 2:**

Find the square root of $15x^2-2x-24=0$.

Answer:

The equation becomes: $$x^2-2x-360=0$$ $$(x+18)(x-20)=0$$ $x=-18$ and $x=20$.

Then we will use the abc formula.

**Example 3:**

From example 1, determine the root with the formula abc.

Answer:

$$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ $$x=\frac{-3 \pm \sqrt{9-8}}{2}$$ $$x=\frac{-3 \pm 1}{2}$$ $$x=\frac{-3+1}{2}=-1$$ and $$x=\frac{-3-1}{2}=-2$$

This is the basic material for quadratic equations. That is all and thank you.