Help please!

Question

determine the value of 'k' that makes each quadratic a perfect square trinomial.

a) x^2 + 14x + k

b) 4x^2 - 28x + k

Answer 1

a) The quadratic x² + 14x +  k

To change the expression into a perfect square trinomial add (half the x coefficient)² .

 Here x coefficient = 14. so, (half the x coefficient)² = (14/2)²= 49

Replace with 49 for k.

Then the quadratic becomes x² + 14x + 49 

= x² + 2(7)x + 7²

Apply the formula (a + b)² = a² + 2ab + b²

x² + 14x + 49 = (x + 7)²

Solution k = 49.

Answer 2

b)

The quadratic 4x² - 28x +  k

Take out common factor.

= 4(x² - 7x +  k/4)

To change the expression (x² - 7x) into a perfect square trinomial add (half the x coefficient)².

 Here x coefficient = -7. so, (half the x coefficient)² = (-7/2)²= 49/4

Replace with 49/4 for k/4.

= 4(x² - 7x +  49/4)

Apply the formula (a + b)² = a² + 2ab + b²

a = x, b = 7/2

= 4[(x)² - 2(7/2)(x) + (7/2)²]

= 4[x - (7/2)]² 

= (2x - 7)²

Solution k = 49.