(x-3/2)^2=5/4

2 min read Jun 17, 2024

Solving the Equation: (x - 3/2)^2 = 5/4

This equation involves a squared term, so we'll use the square root property to solve for x.

Step 1: Take the Square Root of Both Sides

The square root property states that if a² = b, then a = ±√b. Applying this to our equation:

√[(x - 3/2)²] = ±√(5/4)

Step 2: Simplify

This simplifies to:

x - 3/2 = ±√(5/4)

Step 3: Isolate x

Add 3/2 to both sides of the equation:

x = 3/2 ±√(5/4)

Step 4: Simplify the Radical

We can simplify the radical by taking the square root of the numerator and denominator separately:

x = 3/2 ± √5 / √4

x = 3/2 ± √5 / 2

Step 5: Combine Terms

Since both terms have a common denominator, we can combine them:

x = (3 ± √5) / 2

Solution

Therefore, the solutions to the equation (x - 3/2)² = 5/4 are: