(x+1)^2-25/9=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (x+1)^2 - 25/9 = 0

This article will guide you through the process of solving the quadratic equation (x+1)^2 - 25/9 = 0. We'll utilize the principles of algebra to isolate 'x' and find its solutions.

Step 1: Isolate the Squared Term

Begin by adding 25/9 to both sides of the equation to isolate the squared term:

(x+1)^2 = 25/9

Step 2: Take the Square Root

Next, take the square root of both sides of the equation. Remember that taking the square root introduces both positive and negative solutions:

x + 1 = ±√(25/9)

Step 3: Simplify the Square Root

Simplify the square root:

x + 1 = ±5/3

Step 4: Isolate 'x'

Finally, subtract 1 from both sides to isolate 'x':

x = -1 ± 5/3

Step 5: Find the Solutions

Now, we have two possible solutions:

x = -1 + 5/3 = 2/3
x = -1 - 5/3 = -8/3

Therefore, the solutions to the quadratic equation (x+1)^2 - 25/9 = 0 are x = 2/3 and x = -8/3.