x^2+16=-10x?

Set equal to zero first:
x^2+10x+16=0
Factor
(x+8)(x+2)=0

set both factors equal to 0
x+8=0 or x+2=0
so x=-8 or -2 (there are two answers that work)

Put the x's on the same side.

x^2 + 10x + 16 = 0
(x + 2)(x + 8) = 0

Use the null factor law.

x + 2 = 0 or x + 8 = 0
x = -2 or x = -8

x^2 + 16 = - 10x

=> x^2 + 10x + 16 = 0

NOW LOOK here, 16 x 1 = 16 ; 16 = 8 x 2 & 10 = 8 + 2

so we have,

x^2 + 8x + 2x + 16 = 0

=> x(x + 8) + 2 (x + 8) = 0

=> (x + 8)(x + 2) = 0

=> x = - 8 or - 2

ANSWERS : x = - 2, - 8

/
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x=-2,-8

{sq}=square root

x^2+10x+16=0
x=[(-10)+-{sq}(10^2-4(1)(16))]/2

x=[-10+-{sq}(36)]/2

x=[-10+-(6)]/2

x=(-10+6)/2, (-10-6)/2

x=-2, -8

x² + 10x + 16 = 0
(x + 8)(x + 2) = 0
x = - 8 , x = - 2

x^2+16=-10x
x^2 + 10x + 16 = -10x + 10x (Adding both sides by 10x)
x^2 + 10x + 16 = 0
(x + 2) (x + 8) = 0 (Factorising the above equation)
Therefore x = -2 or -8

x^2 + 16 = -10x
x^2 + 10x + 16 = 0
x^2 + 8x + 2x + 16 = 0
(x^2 + 8x) + (2x + 16) = 0
x(x + 8) + 2(x + 8) = 0
(x + 8)(x + 2) = 0

x + 8 = 0
x = -8

x + 2 = 0
x = -2

∴ x = -8 , -2

Move everything to the left, giving:
x^2 - 10x + 16 = 0
Then, factor it out (find what two numbers add up to -10, and multiply together to give 16?)

Since it's summer, I'll answer it too.
The two numbers are -2 and -8. So, you should get
(x-2)(x-8) = 0

If you don't understand any of this, tell your teacher. They will be able to do a better job.