x^2+8x=11
Take half of the coefficient (8) of x and square it. Result: 16.
x^2+8x=11 Add 16 to x^2+8x, and then subtract 64 from the result:
x^2 + 8x + 16 - 16 = 11
Recognize that the first 3 terms can be rewritten as (x+4)^2.
Then:
(x+4)^2 - 16 = 11, or (x+4)^2 = 27
Answer: Add 16, and then subtract 16, as shown.
Solve for x? find the sqrt of both sides: x+4 = plus or minus 3sqrt(3)
Then x = -4 plus or minus 3sqrt(3)