(x-5)2=(x+10)2

Assuming you mean (x - 5)^2 = (x + 10)^2.

Method 1 (square roots): |x - 5| = |x + 10| This gives two cases:

• x - 5 = x + 10 → -5 = 10 (impossible)
• x - 5 = -(x + 10) → 2x = -5 → x = -5/2

Method 2 (expand and equate): x^2 - 10x + 25 = x^2 + 20x + 100 -10x + 25 = 20x + 100 -30x = 75 x = -5/2

Answer: x = -5/2.