xsquared + 8x + 16 = 5?

Question

how do i solve this ?

Answer 1

x² + 8x + 16 = 5

Subtract 5 from both sides:
x² + 8x + 16 - 5 = 5 - 5
x² + 8x + 11 = 0

Use the quadratic formula and simplify:
x = [-8 ± sqrt(64 - 4(11))] / 2
x = [-8 ± sqrt(20)] / 2
x = [-8 ± sqrt(4*5)] / 2
x = [-8 ± 2sqrt(5)] / 2
x = -4 ± sqrt(5)

Answer 2

First, move the 5 over to the left and collect terms

x^2 + 8x + 11 = 0

You'll need to use the quadratic formula for this one.

x = (-8 +- sqrt(64-44))/2

x = -8 +- sqrt (20)/2

x = -8 +- 2sqrt (5)/2

So, your 2 solutions are:

x = -4 + sqrt(5) and x= -4 - sqrt(5)

Answer 3

x^2 + 8x + 16 = 5

The left hand side is a perfect square (x + 4)^2 so:
(x + 4)^2 = 5
x = SQRT(5) - 4

Answer 4

x^2 + 8x + 16 = 5
LHS is a perfect square, so
(x + 4)^2 = 5
or
x + 4 = +or- sqrt(5) = + or - 2.24
x = -4 + 2.24 or -4 -2.24
x = -1.76 or - 6.24
or x =