(x-1)^2=-4

less than a minute read Jun 17, 2024

Solving the Equation (x-1)^2 = -4

This equation involves a squared term and a negative constant on the right-hand side, which suggests we'll be dealing with imaginary numbers. Let's break down the steps to solve it:

1. Isolate the Squared Term

The equation is already in this form, with the squared term isolated:

(x-1)^2 = -4

2. Take the Square Root of Both Sides

Remember that taking the square root introduces both positive and negative solutions:

√((x-1)^2) = ±√(-4)

This simplifies to:

x - 1 = ±2i (where 'i' represents the imaginary unit, √-1)

3. Solve for x

Add 1 to both sides of the equation:

x = 1 ± 2i

Solutions

Therefore, the solutions to the equation (x-1)^2 = -4 are:

x = 1 + 2i
x = 1 - 2i

These are complex numbers with a real part of 1 and an imaginary part of ±2.