Question

I need help on this problem.

Answer 1

x^2+7x +49/4 and (x+7/2)^2

x^2+bx +b²/4 and (x+b/2)^2

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