Types of Equations

In our previous post, we discussed on equations especially linear equations, now we'll be exposing you to different types of equations in maths... Here are the types of equations:
(1)Linear equation
(2)Quadratic equation
(3)Polynomial equation
(4)Trigonometric equation
(5)Radical equation
(6)Exponential equation

Solving equationsmeans to find the value or set of values of unknown variable contained in it.
Let us go ahead in this chapter and learn more about different types of differential equations and sample problems based on those

Different Types of Equations

An equation is an important part of calculus, which comes under mathematics. It helps us to solve many problem.

Types of Algebraic Equations

Lets discuss different types of algebraic equations:

1) Linear Equations:
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The graph of linear equation is a straight line if there are two variables.
General form of the linear equation with two variables:
y = mx + c
Where ,m is known as slope and c at that point on which it cut y axis.
Linear equations with different variables:
a)The equation with one variable:
An equation who have only one variable.
Examples:
1. 8a - 8 = 0
2. 9a = 72.

b)The equation with two variables:
An equation who have only two types of variable in the equation.
Examples:
1. 7x + 7y = 12
2. 8a - 8d = 74
3. 9a + 6b - 82 = 0.

c)The equation with three variables:
An equation who have only three types of variable in the equation.
Examples:
1. 5x + 7y - 6z = 12
2.13a - 8b + 31c = 74
3. 6p + 14q -7r + 82 = 0.

2) Radical Equations:
An equation whose maximum exponent on the variable is$\frac{1}{2}$and have more than one term or we can say that a radical equation is an equation in which the variable is lying inside a radical symbol usually in a square root.
Examples
1.{x} + 10 = 26
2.{x^2 - 5} + x - 1

3) Quadratic Equations:
Quadratic equation is the second degree equation in one variable contains the variable with an exponent of 2.

The general form:
ax2+ bx + c = 0,
Examples of Quadratic Equations:
1. 8x2+ 7x - 75 = 0
2. 4y2+ 14y - 8 =0
3. 5a2- 5a = 35

4) Exponential Equations
An equation who have variables in the place of exponents. Exponential equation can be solved using the property: a^x = a^y => x = y. Examples:
1. ab= 0 Here "a" is base and "b" is exponent.
2. 4x=0
3. 8x= 32.

5) Rational Equations:
A rational equation is one that involves rational expressions. Example: {x}{2} = {x + 2}{4}.

Types of Math Equations
Here, we will solve some algebraic equations:
Solved Examples
Question 1:
Solve the quadratic equation

x2+ 6x - 27 = 0.

Solution:
Given quadratic equation: x2+ 6x - 27 = 0
x2+ 6x - 27 = 0
x2+ 9x - 3x - 27 = 0
=> x(x + 9) - 3(x - 9) = 0
=> (x - 3)(x + 9) = 0
=> either x - 3 = 0 or x + 9 = 0
=> x = 3 or x = -9
The values of x are (3, -9).

Question 2:

Solve 8x= 32

Solution:
Given equation is 8x= 32.
=> 8x= 32
or (23)x= 25
or 23x= 25
Since the bases of the equation are same, set the exponents equal to one another:
=> 3x = 5
x = {5}{3}

Question 3

Solve $\sqrt{x + 3}$ = 2

Solution:
Given equation is {x + 3} = 2
=> {x + 3} = 2
To isolate the x, squaring both side
=> x + 3 = 4
x = 4 - 3
x = 1