(x+10)^2=(x-9)^2

2 min read Jun 16, 2024

Solving the Equation: (x+10)^2 = (x-9)^2

This equation presents a simple yet effective example of how to solve equations involving squares. Here's a step-by-step guide:

Understanding the Equation

The equation (x+10)^2 = (x-9)^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
- (x-9)^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 = (x-9)^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 = (x-9)^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.