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# What are the factors of x^{2} - 100 = 0?

**Solution: **

Given:

Quadratic equation is x^{2} - 100 = 0 with degree 2.

As we know that the standard form of the quadratic equation is ax^{2} + bx + c = 0 --- (1)

**So comparing the given equation with the equation (1) we get,**

a = 1, b = 0, c = 100

**Now solving the quadratic equation by factorising**

⇒ x^{2} - 100 = 0

**For factorising first split the middle term 0 as -10x and 10x as**

-10x + 10x = 0 and (-10x) (10x) = -100x^{2}

⇒ x^{2} - 10x + 10x -100 = 0

⇒ x(x - 10) + 10(x - 10) = 0

⇒ (x + 10)(x - 10) = 0

**We can understand by the given example:**

**Example: **

What is the factors of n^{2} - 25 = 0?

Given:

Equation is n^{2} - 25 = 0

By solving we get,

⇒ n^{2} = 25

⇒ √n^{2} = √(25) (Applying square root both sides)

⇒ n = √(5)(5)

⇒ n = ±5

⇒ n = 5 and n = -5

**⇒ The factors are (n - 5) and (n + 5)**

## What are the factors of x^{2} - 100 = 0?

**Summary:**

By solving the given quadratic equation x^{2 }- 100 with factorising method we get the two linear factors as (x + 10) and (x - 10).

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