(x-4)^2+(x+9)^2=2x^2

2 min read Jun 17, 2024

Solving the Equation (x-4)^2 + (x+9)^2 = 2x^2

This article explores the solution to the equation (x-4)^2 + (x+9)^2 = 2x^2. We will break down the steps involved in solving this equation and arrive at the final solution.

Expanding the Equation

First, we expand the squares on the left-hand side of the equation:

(x-4)^2 = x^2 - 8x + 16 (x+9)^2 = x^2 + 18x + 81

Substituting these values back into the original equation, we get:

x^2 - 8x + 16 + x^2 + 18x + 81 = 2x^2

Simplifying the Equation

Combining like terms on the left-hand side of the equation, we have:

2x^2 + 10x + 97 = 2x^2

Subtracting 2x^2 from both sides, the equation simplifies to:

10x + 97 = 0

Solving for x

To isolate x, we subtract 97 from both sides:

10x = -97

Finally, dividing both sides by 10, we find the solution for x:

x = -9.7

Conclusion

Therefore, the solution to the equation (x-4)^2 + (x+9)^2 = 2x^2 is x = -9.7.