Respuesta :
Answer:
200√5
Step-by-step explanation:
20 = 2 x 2 x 5
√20 = 2√5
40 = 2 x 2 x 10
√40 = 2√10
2√20
= 2 x 2√5
= 4√5
5√40
= 5 x 2√10
= 10√10
2√20 x 5√40
= 4√5 x 10√10
{ √10 = √5 x √2 }
= 4√5 x 10 x √5 x √2
= 10 x 4 x √2 x √5 x √5
{ √5 x √5 = 5 }
= 10 x 4 x √2 x 5
= 10 x 4 x 5 x √2
= 200√5
Hence simplified.
Answer: Simplifying
x2 + 400x + -40000 = 0
Reorder the terms:
-40000 + 400x + x2 = 0
Solving
-40000 + 400x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '40000' to each side of the equation.
-40000 + 400x + 40000 + x2 = 0 + 40000
Reorder the terms:
-40000 + 40000 + 400x + x2 = 0 + 40000
Combine like terms: -40000 + 40000 = 0
0 + 400x + x2 = 0 + 40000
400x + x2 = 0 + 40000
Combine like terms: 0 + 40000 = 40000
400x + x2 = 40000
The x term is 400x. Take half its coefficient (200).
Square it (40000) and add it to both sides.
Add '40000' to each side of the equation.
400x + 40000 + x2 = 40000 + 40000
Reorder the terms:
40000 + 400x + x2 = 40000 + 40000
Combine like terms: 40000 + 40000 = 80000
40000 + 400x + x2 = 80000
Factor a perfect square on the left side:
(x + 200)(x + 200) = 80000
Calculate the square root of the right side: 282.842712475
Break this problem into two subproblems by setting
(x + 200) equal to 282.842712475 and -282.842712475.
Subproblem 1
x + 200 = 282.842712475
Simplifying
x + 200 = 282.842712475
Reorder the terms:
200 + x = 282.842712475
Solving
200 + x = 282.842712475
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-200' to each side of the equation.
200 + -200 + x = 282.842712475 + -200
Combine like terms: 200 + -200 = 0
0 + x = 282.842712475 + -200
x = 282.842712475 + -200
Combine like terms: 282.842712475 + -200 = 82.842712475
x = 82.842712475
Simplifying
x = 82.842712475
Subproblem 2
x + 200 = -282.842712475
Simplifying
x + 200 = -282.842712475
Reorder the terms:
200 + x = -282.842712475
Solving
200 + x = -282.842712475
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-200' to each side of the equation.
200 + -200 + x = -282.842712475 + -200
Combine like terms: 200 + -200 = 0
0 + x = -282.842712475 + -200
x = -282.842712475 + -200
Combine like terms: -282.842712475 + -200 = -482.842712475
x = -482.842712475
Simplifying
x = -482.842712475
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {82.842712475, -482.842712475}
