(x-5)^2=(x+12)^2

2 min read Jun 17, 2024

Solving the Equation: (x-5)^2 = (x+12)^2

This equation presents a scenario where we need to find the value(s) of x that satisfy the given condition. Let's break down the solution step-by-step:

1. Expanding the Squares

We begin by expanding both sides of the equation using the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2

Left Side: (x - 5)^2 = x^2 - 10x + 25
Right Side: (x + 12)^2 = x^2 + 24x + 144

Now our equation becomes: x^2 - 10x + 25 = x^2 + 24x + 144

2. Simplifying the Equation

Next, we can simplify the equation by bringing all terms to one side:

Subtracting x^2 from both sides: -10x + 25 = 24x + 144
Subtracting 24x from both sides: -34x + 25 = 144
Subtracting 25 from both sides: -34x = 119

3. Isolating x

Finally, we isolate x by dividing both sides by -34:

x = 119 / -34
x = -3.5

Conclusion

Therefore, the solution to the equation (x - 5)^2 = (x + 12)^2 is x = -3.5. This value of x satisfies the original equation, making it the only solution.