(x+3)^2=36

2 min read Jun 16, 2024
(x+3)^2=36

Solving the Equation (x+3)^2 = 36

This equation involves a squared term, which means we need to consider both positive and negative solutions. Let's break down the steps to solve it:

1. Taking the Square Root

First, we need to isolate the squared term by taking the square root of both sides of the equation:

√((x+3)^2) = ±√36

This gives us:

x + 3 = ±6

2. Isolating x

Next, we need to isolate 'x' by subtracting 3 from both sides:

x = -3 ±6

3. Finding the Solutions

Now, we have two possible solutions:

  • x = -3 + 6 = 3
  • x = -3 - 6 = -9

Therefore, the solutions to the equation (x+3)^2 = 36 are x = 3 and x = -9.

Verification

We can verify our solutions by plugging them back into the original equation:

  • For x = 3: (3 + 3)^2 = 6^2 = 36
  • For x = -9: (-9 + 3)^2 = (-6)^2 = 36

Both solutions satisfy the original equation.

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