How can we factorize 8x^2+8sqrt2x+4=0 to solve it?

2 Answers
Dec 4, 2017

8x^2+8sqrt2x+4=8(x+1/sqrt2)^2=0 and
solution is +-1/sqrt2

Explanation:

8x^2+8sqrt2x+4=0 can be written as

8(x^2+sqrt2x)+4=0

or 8(x^2+2xx1/sqrt2x+(1/sqrt2)^2-(1/sqrt2)^2)+4=0

or 8(x+1/sqrt2)^2-8xx1/2+4=0

or 8(x+1/sqrt2)^2=0 i.e.

(x+1/sqrt2)^2=0 or x+1/sqrt2=0

As this is an equation, we get x=-1/sqrt2 as solution.

May 26, 2018

Therefore the factors are:

(2sqrt2x + 2).(2sqrt2x + 2)

Value of x = +-1/sqrt2

Explanation:

Split the middle term so that it adds up to 8sqrt2x and the same two factors when multiplied gives 8 xx 4 = 32

Step 1: Find the multiples of 32
32 = 2 xx 2 xx 2 xx 2 xx 2 = 4sqrt2 xx 4sqrt2

Now adding 4sqrt2 + 4sqrt2 = 8sqrt2

So now we have two common factors satisfying the above and these are 4sqrt2 and 4sqrt2

Step 2: Write 8x^2 in terms of sqrt2
8x^2 = (2sqrt2) ^2x^2

Step 3: Re-write the equation

(2sqrt2)^x^2 +8sqrt2x + 4

(2sqrt2)^2x^2 + 4sqrt2x + 4sqrt2x +4

2sqrt2x.(2sqrt2x + 2) + 2.(2sqrt2x +2)

(2sqrt2x + 2).(2sqrt2x + 2)

Therefore the factors are:

(2sqrt2x + 2).(2sqrt2x + 2)

Value of x = +-1/sqrt2