Solving the Equation: (x+10)^2 = (x9)^2
This equation presents a simple yet effective example of how to solve equations involving squares. Here's a stepbystep guide:
Understanding the Equation
The equation (x+10)^2 = (x9)^2 involves squaring both sides. This means we need to expand the squares and then solve for x.
Solving the Equation

Expand the squares:
 (x+10)^2 = x^2 + 20x + 100
 (x9)^2 = x^2  18x + 81

Set the expanded equations equal to each other:
 x^2 + 20x + 100 = x^2  18x + 81

Simplify by subtracting x^2 from both sides:
 20x + 100 = 18x + 81

Combine like terms:
 38x = 19

Isolate x by dividing both sides by 38:
 x = 19 / 38

Simplify the fraction:
 x = 1/2
The Solution
Therefore, the solution to the equation (x+10)^2 = (x9)^2 is x = 1/2.
Checking the Solution
It's always good practice to check our answer by plugging it back into the original equation:
 (1/2 + 10)^2 = (9.5)^2 = 90.25
 (1/2  9)^2 = (9.5)^2 = 90.25
Since both sides are equal, we have verified that our solution is correct.
Conclusion
By expanding the squares, combining like terms, and isolating the variable, we successfully solved the equation (x+10)^2 = (x9)^2, arriving at the solution x = 1/2. Remember to always check your solution by plugging it back into the original equation to ensure accuracy.