Answer:
The Solution of the equation is
x= 5 ± [tex]2\sqrt{5}[/tex]
Step-by-step explanation:
We are supposed to find the solution of the equation by completing square method
our given equation is
2x² + 20x + 10 = 0
Dividing whole equation by 2
we will get
x² + 10 x + 5 = 0
Now we will write the middle term in factor form to see what we will be needing to make it perfect square
it would be written as
x² + 2(5) x + 5 = 0
Now adding 20 on both sides we get
x² + 2(5) x + 5 + 20 = 20
x² + 2(5) x + 25 = 20
(x)² + 2(5) x +(5)² = 20
Now we have the form of a²+2(a)(b) + b²
And also we know that
a²+2(a)(b) + b² = (a+b)²
So our equation becomes
(x+5)² = 20
Taking square root of both sides it becomes
[tex]\sqrt{(x+5)^{2} }=\sqrt{20}[/tex]
square cuts out with square root so
it becomes
x+5 = ±[tex]\sqrt{20}[/tex]
We know that [tex]\sqrt{20}=2\sqrt{5}[/tex]
So it becomes
x+5 =± [tex]2\sqrt{5}[/tex]
Subtracting 5 from both sides
it becomes
x= 5 ± [tex]2\sqrt{5}[/tex]
So
The Solution of the equation is
x= 5 ± [tex]2\sqrt{5}[/tex]
