Equations

An equation is a mathematical statement that has two expressions separated by an equal sign. Solving an equation means manipulating the expressions and finding the value of the variables.

An equation in one variable has a single unknown quantity called a variable represented by a letter. Eg: ‘x’, where ‘x’ is always to the power of 1. This means there is no ‘ x² ’ or ‘ x³ ’ in the equation.

5x + 2 = 2x + 17
Subtract 2x from both sides:
5x + 2 - 2x = 2x + 17 - 2x
Simplify both sides:
3x + 2 = 17
Subtract 2 from both sides:
3x + 2 - 2 = 17 - 2
Simplify both sides:
3x = 15
Divide both sides by 3:
Simplify both sides:
x = 5

Zero Product

(3x - 2)(x + 1) = 0

Use the principle of zero product, which says, if ab = 0 , either a, b, or both must be equal to zero.

3x - 2 = 0 0x + 1 = 0
3x = 2 x = -1
x = (2/3)



The solutions are : -1 and 2/3

Quadratic equation

A general quadratic equation can be written in the form, where x represents a variable or an unknown and a, b, and c are constants with a ≠ 0. (If a = 0, the equation is a linear equation .)

Polynomial equation solved by factoring :

3 − 11/2 x − 5x² = 0
5x² +11/2 x − 3= 0
5x² +11/2 x− 3 = 0
(5x − 2 )(2x + 3)= 0
So , the solutions are 2/5and −3/2

Solved by completing the square

Completing the square is a technique for converting a quadratic polynomial of the form

Ax^2+bx+c to a(x-h)^2+k

3x²+12x+27 = 3(x²+4x+9 )
= 3((x+2)²+5)
=3(x+2)²+5

By Parameswari & Sivapriya 2nde 2 =)