# How to Solve Any Quadratic Equation Using The “Almighty” Formula #### There are four different methods that can be used to solve a quadratic equation. Which are:

1. Factorization;
2. Completing the square;
4. Graphical solution.

Each of the four methods above can be used to solve specific types of quadratic equations, however, our main focus shall be to apply the general quadratic formula also known as the “Almighty formula”.

As the alias implies, it can be used to solve any standard quadratic equation. This formula works where all else have failed.

EXAMPLE: Solve 4x2-11x – 21 = 0

Solution: Compare the given equation with the standard quadratic equation: ax2 + bx + c = 0

#### The Almighty Formula(General Quadratic Formula)

A standard quadratic formula is of the form ax2 + bx + c = 0

katex is not defined

Where:

katex is not defined are coefficients of katex is not defined and katex is not defined respectively;
katex is not defined is a constant and;
katex is not defined

In solving for katex is not defined, the formula states that:

katex is not defined

SO, LET’S SEE AN EXAMPLE:

EXAMPLE :

Solve the equation katex is not defined using the general quadratic(Almighty) formula.

SOLUTION TO EXAMPLE:

The equation is:

katex is not defined

So, that means:

katex is not defined katex is not defined and katex is not defined

Therefore, substituting the values of: katex is not defined katex is not defined and katex is not defined

into the formula katex is not defined gives:

katex is not defined

katex is not defined

katex is not defined

katex is not defined

Hence:

katex is not defined

katex is not defined OR katex is not defined

katex is not defined OR katex is not defined

katex is not defined OR katex is not defined

ACTIVITY:

Solve the equation katex is not defined using the general quadratic(Almighty) formula.

## DILIGENTLY ATTEMPT TO SOLVE THE QUESTION FIRST. WHEN YOU ARE DONE, CLICK “VIEW SOLUTION NOW” TO SEE IF YOU GOT IT.

SOLUTION TO ACTIVITY:

The equation is:

katex is not defined

This means that:

katex is not defined katex is not defined and katex is not defined

Therefore, substituting the values of katex is not defined katex is not defined and katex is not defined into the formula

katex is not defined

Gives:

katex is not defined

Therefore:

katex is not defined

katex is not defined

katex is not defined

katex is not defined

This implies that:

katex is not defined OR katex is not defined

katex is not defined OR katex is not defined