#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Pair of Linear Equations in Two Variables

- Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient

##### Arithmetic Progressions

##### Quadratic Equations

- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Quadratic Equations Examples and Solutions

##### Polynomials

##### Geometry

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem Or Thales Theorem
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity Triangle Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity
- Ratio of Sides of Triangle

##### Constructions

##### Trigonometry

##### Heights and Distances

##### Trigonometric Identities

##### Introduction to Trigonometry

##### Statistics and Probability

##### Probability

##### Statistics

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Mensuration

##### Areas Related to Circles

##### Surface Areas and Volumes

#### description

- method of completing the square

#### notes

In the previous section, you have learnt one method of obtaining the roots of a quadratic equation. In this section, we shall study another method. To implement this method we have certain steps to follow. We will understand the steps with `2x^2+7x-9=0` this example-

1) Make the coefficient of ` x^2` as 1. For that we have to divide the whole equation with the coefficient of `x^2`. In the above example coefficient of `x^2` is 2 so will divide the equation with 2, we get, `x^2+"7x"/2-9/2=0`

2) After that take the constant to RHS. So we get `x^2+"7x"/2=9/2`.

3) Now take the square of the coefficient of x after multiplying with `1/2`, and then add that number to both the sides i.e add: `(1/2× "coefficient" "of" x)^2`

Coefficient of x here is `7/2, (1/2×7/2)^2 = (7/4)^2`

by adding `(7/4)^2` both the sides we get, `x^2+"7x"/2+(7/4)^2 = 9/2+(7/4)^2`

4) Use `(a+b)^2` or `(a-b)^2`

`x^2+"7x"/2+(7/4)^2 = 9/2+(7/4)^2`

By obervation we get, `c= 9/2 + 49/16`

`(x+7/4)^2= (72+49)/16`

`(x+7/4)^2= 121/16`

`x+7/4 = + or - sqrt 121/16`

`x+7/4 = + or - 11/4`

`x+7/4 = 11/4 or -11/4`

`x=11/4-7/4 or -11/4-7/4`

`x= 4/4 or -18/4`

`x= 1 or -9/2`

Thus, the roots of `2x^2+7x-9=0` are `1 or -9/2`

We can solve more examples using complete square method to understand easily.