Respuesta :
Answer:
To create a perfect square of given expression,
[tex]5x^2+15x[/tex]On solving the above expression we get,
[tex]=5(x^2+3x)[/tex]we have that,
[tex](x+a)^2=x^2+2ax+a^2[/tex]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,
[tex]=5(x^2+3x+2.25)[/tex]In general, we adding 11.25 (that is, 2.25x5=11.25) to the given expression.
we get,
[tex]=5(x+1.5)^2[/tex]Multiply 5 to the above equation, we get
[tex]=5^2(x+1.5)^2[/tex][tex]=(5x+7.5)^2[/tex]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.
