Question

Which of the following are solutions to the quadratic equation below?

Check all that apply.
x+8x+16=2
A. 2
B. 2-4
C. 4
D. -√2-4
E. √2 +4
F. 1

Answer 1

Hi,

Explanation:

To find the solutions to the quadratic equation x² + 8x + 16 = 2, we need to first rewrite it in standard quadratic form (ax² + bx + c = 0):

x² + 8x + 16 - 2 = 0

x² + 8x + 14 = 0

Now, you can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 8, and c = 14. Plugging these values into the quadratic formula:

x = (-8 ± √(8² - 4*1*14) / (2*1)

x = (-8 ± √(64 - 56)) / 2

x = (-8 ± √8) / 2

x = (-8 ± 2√2) / 2

Now, simplify:

x = -4 ± √2

So, the solution to the quadratic equation x² + 8x + 14 = 0 is

D. -√2 - 4

`x^2+8x+16=2\\x^2+2*4x+4^2=2\\(x+4)^2=2\\\\(x+4-√(2) )(x+4+√(2) )=0\\Solutions\ are\ x=-4+√(2) \ and\ x=-4-√(2) \\Answer : \ D \ is \ one\ solution\ of\ the\ equation.`