Final answer:
To solve the polynomial equation x²+5x=100 using the Chinese method, rewrite the equation as (x+2.5)²=100 and take the square root of both sides.
Step-by-step explanation:
We can solve the equation x²+5x=100 using the Chinese method of solving polynomial equations. This method involves recognizing that the left side of the equation is a perfect square. In this case, we can rewrite the equation as (x+2.5)²=100.
Next, we take the square root of both sides to solve for x. Taking the square root of the right side gives us ±10. Taking the square root of the left side gives us x+2.5. So x+2.5=±10. Finally, we solve for x by subtracting 2.5 from both sides, giving us x=-2.5±10.