Help on algebra a(x-h)^2+k complete square?

Question

what is 7x^2+7x+7 in a(x-h)^2+k form?

Answer 1

7x² + 7x + 7

Take out common term 7.

7(x² + x + 1).

This expression it can be written as 7(x² + x + 1 + 2x - 2x).

7(x² - 2x + 1 + 3x)

7[(x² - 2(x)(1) + 1²) + 3x)].

Mathematical formula: (a² - 2ab + b²) = (a - b)²

7(x - 1)² + 21x

Compare above form with standard form a(x-h)²+k and write the coefficients.

So, a = 7, h = 1 and k = 21x.

Answer 2

The expression is 7x² + 7x + 7.

Common out 7 from the expression.

7(x² + x + 1).

 To change the expression : x² + x + 1, into a perfect square trinomial add and subtract (half the x coefficient)² to the expression.

 Here x coefficient = 1. so, (half the x coefficient)² = (1/2)²= 1/4.

Add  and subtract 1/4 to the expression.

= 7(x² + x  + 1/4 + 1 - 1/4)

= 7[ (x + 1/2)² + 1 - 1/4 ]

= 7[ (x + 1/2)² + 3/4 ]

= 7(x + 1/2)² + (7 * 3/4)

= 7(x + 1/2)² + (21/4).

Compare the above equation with a(x - h)² + k.

a = 7, h = - 1/2, and k = 21/4.