(x+a)^2=b

2 min read Jun 17, 2024

Solving the Equation (x + a)^2 = b

This equation represents a common algebraic problem that requires a few steps to solve for the unknown variable, 'x'. Let's break it down:

Understanding the Equation

The equation (x + a)^2 = b is a quadratic equation in disguise. It involves squaring a binomial (x + a) and setting it equal to a constant value 'b'.

Solving for x

Take the square root of both sides:

To eliminate the square, we take the square root of both sides of the equation: √[(x + a)^2] = ±√b

Remember to include both positive and negative square roots because squaring a positive or negative number results in a positive value.
Simplify:

This simplifies to: x + a = ±√b
Isolate x:

Subtract 'a' from both sides to isolate 'x': x = -a ±√b

Example

Let's solve the equation (x + 3)^2 = 16:

Take the square root of both sides: √[(x + 3)^2] = ±√16
Simplify: x + 3 = ±4
Isolate x: x = -3 ± 4

This gives us two possible solutions:

x = -3 + 4 = 1
x = -3 - 4 = -7

Conclusion

The equation (x + a)^2 = b can be solved by following these steps: taking the square root of both sides, simplifying, and isolating the variable 'x'. This results in two possible solutions due to the nature of square roots. By understanding these steps, you can confidently solve any equation of this form.