Question

What should be done to 5x^2 +15x in order to create a perfect square?

Answer 1

To create a perfect square of given expression,

`5x^2+15x`

On solving the above expression we get,

`=5(x^2+3x)`

we have that,

`(x+a)^2=x^2+2ax+a^2`

To create a perfect square: add ( half the coefficient of the x- term )²

Coefficient of x term is 3

half the coefficient of the x- term is 1.5

( half the coefficient of the x- term )² is 2.25

Add 2.25 to the quadratic expression inside the bracket, we get,

`=5(x^2+3x+2.25)`

In general, we adding 11.25 (that is, 2.25x5=11.25) to the given expression.

we get,

`=5(x+1.5)^2`

Multiply 5 to the above equation, we get

`=5^2(x+1.5)^2`
`=(5x+7.5)^2`

Based on the above calculation, we adding 11.25 and multiplying the expression by 5 in order to create a perfect square.

Adding 11.25 and multiplying the expression by 5 in order to create a perfect square.