What number should be added to both sides of the equation to complete the square? x2 + 3x = 6

Solution:

For completing the square, we follow these steps:

1. First, divide the coefficient of the term x by 2 and square the result.

2. This number should be added to both sides of the equation

Given equation is x2 + 3x = 6----(1)

By completing the square method if the coefficient of x is 3.

Divide this number by 2 then square the result

(3 / 2)2 = 9 / 4 i the number to be added on both the sides for completing the square

Equation (1) can be written as

x2 + 3x + (9/4) = 6 +(9/4) {On adding 9/4 on both the sides}

x2 + 3x + (9/4) = 6 + (9/4)

x2 + 2 . (3/2). x + (3/2)2 = (24 + 9)/4

(x + (3/2))2 = 33/4

Take square root on both the sides of the above equation 

x + (3/2) = ±√33/4

The number should be added to both sides of the equation to complete the square of the equation

x2 + 3x = 6 is 9 / 4

What number should be added to both sides of the equation to complete the square? x2 + 3x = 6

Summary:

9/4 should be added to both sides of the equation to complete the square x2 + 3x = 6.

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