Answer:
x^2+7x +49/4 and (x+7/2)^2
x^2+bx +b²/4 and (x+b/2)^2
Step-by-step explanation:
Given the expression
x^2+7x+c
We need to find the constant that completes the expression
Take the half of the cpeffiecient of x = 7/2
Taking the square of the result
Square of the result = (7/2)^2
Hence c = (7/2)^2
The expression becomes;
x^2 + 7x + (7/2)^2
= x^2+7x +49/4
= (x+7/2)^2
For x^2+bx+d
We need to find the constant that completes the expression
Take the half of the cpeffiecient of x = b/2
Taking the square of the result
Square of the result = (b/2)^2
Hence d = (b/2)^2
The expression becomes;
x^2 + bx + (b/2)^2
= x^2+bx +b²/4
= (x+b/2)^2
