Respuesta :

Answer:

A and B

Step-by-step explanation:

Given

x² + 8x + 16 = 2 ( subtract 16 from both sides )

x² + 8x = - 14

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(4)x + 16 = - 14 + 16

(x + 4)² = 2 ( take the square root of both sides )

x + 4 = ± [tex]\sqrt{2}[/tex] ( subtract 4 from both sides )

x = - 4 ± [tex]\sqrt{2}[/tex], that is

x = - 4 - [tex]\sqrt{2}[/tex] → A

x = - 4 + [tex]\sqrt{2}[/tex] → B

The solutions to the quadratic equation x^2 + 8x + 16 = 2 are

What are the identities that we must use in this equation?

Initially, we must the square of sums identity which is given by:

(a + b)² = a² + 2ab + b²

Then we must the identity that is shown below to split the factors:

a² - b² = (a + b)(a - b)

We can solve the quadratic equation as a shown below:

The quadratic equation is x^2 + 8x + 16 = 2.

We can rewrite and simplify the equation as follows:

x^2 + 2*4*x + 4^2 = 2

⇒ (x - 4)² - 2 = 0

⇒ (x - 4 - √2)(x - 4 +√2) = 0

⇒ x = 4 + √2, x = 4 - √2

Now observe the given options.

We can see that options C and D are the same as the value x that we have found.

Options A and B have values that don't match the value of x.

We have solved the quadratic equation.

Therefore, we have found that the solutions to the quadratic equation x^2 + 8x + 16 = 2 are x = 4 + √2 and x = 4 - √2. The correct answers are options C and D.

Learn more about identities here: https://brainly.com/question/10449635

#SPJ2

Otras preguntas