# Write x^{2} - 2x - 3 = 0 in the form (x - a)^{2 }= b, where a and b are integers

**Solution:**

Given equation is x^{2} - 2x - 3 = 0

Given quadratic equation can be written in the form (x - a)^{2 }= b by following steps:

Take the coefficient of the middle term (-2) and divide it by 2

Then square the result.

Add this number into the equation right after the middle term

Subtract this number after the last term.

Take the middle term and divide by 2……………..-2/2 = -1

Then square the result ……. (-1)^{2} = 1

Add this number into the equation right after the middle term ……

let us proceed accordingly,

x^{2} - 2x + 1 - 3 - 1 = 0

⇒ x^{2} - 2x + 1 = 4

LHS term is in the form of x^{2} - 2 × x × 1 + 1^{2}

= a^{2} - 2ab +b^{2}

But by using standard formula:

a^{2} - 2ab + b^{2} = (a - b)^{2}

⇒x^{2} - 2 × x × 1 + 1^{2} = (x - 1)^{2}

Therefore

x^{2} - 2x + 1 = 4

⇒ (x - 1)^{2} = 4.

## Write x^{2} - 2x - 3 = 0 in the form (x - a)^{2 }= b, where a and b are integers

**Summary:**

The equation x^{2} - 2x - 3 = 0 in the form (x - a)^{2 }= b can be written as (x - 1)^{2} = 4.

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