(√2х+5)²=5²

To solve this equation, we can start by expanding the left side and then setting it equal to the right side:

(√2x + 5)² = 5²

Expanding the left side: (√2x + 5)(√2x + 5) = 25

Using the FOIL (First, Outer, Inner, Last) method: (√2x)(√2x) + (√2x)(5) + (5)(√2x) + (5)(5) = 25

Simplifying: 2x + 5√2x + 5√2x + 25 = 25

Combining like terms: 2x + 10√2x + 25 = 25

Subtracting 25 from both sides: 2x + 10√2x = 0

Now, we can divide both sides of the equation by 2 to simplify it: x + 5√2x = 0

Dividing both sides by x: 1 + 5√2 = 0

Subtracting 1 from both sides: 5√2 = -1

Dividing by 5: √2 = -1/5

Since we cannot have a negative value inside the square root, this equation has no solution.