Question

Solve the following quadratic equation using square roots: (x+6)^2/2=8 .
{10,−22} left brace 10 comma negative 22 right brace {−1.17,−6.83} left brace negative 1.17 comma negative 6.83 right brace ​ {−0.34,−11.66} ​ left brace negative 0.34 comma negative 11.66 right brace {−2,−10} left brace negative 2 comma negative 10 right brace

Answer 1

To solve the quadratic equation using square roots, we first need to isolate the variable x.

Starting with the given equation:

(x+6)^2/2 = 8

We can begin by multiplying both sides of the equation by 2:

(x+6)^2 = 16

Next, we take the square root of both sides of the equation to eliminate the squared term:

sqrt((x+6)^2) = sqrt(16)

(x+6) = ±4

Now, we can solve for x by considering both the positive and negative values of ±4:

For x+6 = 4, we subtract 6 from both sides of the equation:

x = 4 - 6 = -2

For x+6 = -4, we subtract 6 from both sides of the equation:

x = -4 - 6 = -10

Therefore, the solutions to the quadratic equation are x = -2 and x = -10.