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In maths, an equation is a statement that two things are equal. In an equation, there are two expressions, one on each side of the equal to sign.

Variables are the unknown in an equation. An equation could contain one or more unknowns. This process of finding the value of the unknown is called solving the equation.

Simultaneous equations are two equations with two unknowns. They are called simultaneous equations because they must be solved together in order to determine the unknowns.

Quadratic equations

In algebra, a quadratic equation is any equation having the form ax2 + bx + c = 0 . The name quadratic comes from the Latin word Quadratus meaning “square”.

The quadratic equation is univariate as it involves only one unknown. It is a second degree polynomial equation as it contains powers of x that are non negative integers and the greatest power in the equation is 2.

Solving the quadratic equation by factorising

To solve a quadratic equation, we first write it in the form: ax2 + bx + c = 0 and then factorise it.

For example: To solve the quadratic equation x2 - 9x + 20 = 0,

We find two numbers which multiply to give 20 and add up to give 9 viz. 4 and 5. We can now rewrite the equation as

(x - 4) (x - 5) = 0

This implies that either x = 4 or x = 5 for the product to be 0

Completing the square

If the quadratic equation does not factorize then you can solve it using completing the square method.

In this method we write the algebraic expression as a square plus another term. The other term is found by first dividing the coefficient of x by 2, and then squaring it.

For example

Consider the equation x2 + 6x - 2 = 0
Here the coefficient of x is 6. Divide 6 by 2 and square it = 9
Therefore we can rewrite the equation as
(x2 + 6x + 9) - 9 - 2 = 0
(x + 3)2 - 9 - 2 = 0
(x + 3)2 - 11 = 0
(x + 3)2 = 11
x = -3 - square root of 11
x = -3 - 3.31 = -6.31

In this way you can arrive at a formula that works for all quadratic equations using completing the square method. 

You can also solve quadratic equations with the help of a graph. However the most preferred method is the factoring method.

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