Question

Solve the equation by completing the square.  ^x2- 12x = -28

Answer 1

x = 6 + 2√2 and x = 6 - 2√2

Explanation:

Please write the " ^ " symbol between x and 2 here: x^2 - 12x = -28.

Take half the coefficient of x; here that is -6.

Square this, obtaining 36.

Add 36 to, and then subtract 36 from, x^2 - 12x: x^2 - 12x + 36 - 36.

Rewrite x^2 - 12x + 36 as the square of a binomial: (x - 6)^2.

Then rewrite x^2 - 12x = -28 as (x - 6)^2 - 36 = -28.

Simplifying, (x - 6)^2 = 8.

Taking the square root of both sides, x - 6 = plus or minus 2√2.

Then the solutions are x = 6 + 2√2 and x = 6 - 2√2

Answer 2

x^2 -12 x = -28

(-12/2) ^ 2 =36

x^2 -12 x + 36 = -28 + 36

x^2 -12x + 36 = 8

(x-6)^2 = 8

take the square root of each side

x-6 = sqrt (8) x-6 = -sqrt (8)

you get a positive and a negative when taking the square root

x= 6 + sqrt (8)

x = 6 - sqrt (8)

sqrt (8) = 2 sqrt (2)

x= 6 + 2 sqrt (2)

x = 6 - 2 sqrt (2)

Answer:

x= 6 + 2 sqrt (2)

x = 6 - 2 sqrt (2)