%5E2%3D5.jpeg "(x+3)^2=5")
Solving the Equation (x+3)² = 5
This equation involves a squared term, which means we'll need to use the square root to solve for x. Let's break down the steps:
1. Isolate the Squared Term
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Take the square root of both sides: This will remove the square from the left side of the equation.
√((x+3)²) = ±√5
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Simplify: Remember that taking the square root of a squared term results in the absolute value.
|x+3| = ±√5
2. Solve for x
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Consider both positive and negative roots: Because we took the square root, we need to account for both the positive and negative values of √5.
- Case 1: x + 3 = √5
- Case 2: x + 3 = -√5
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Solve for x in each case:
- Case 1: x = √5 - 3
- Case 2: x = -√5 - 3
3. Solutions
Therefore, the solutions to the equation (x+3)² = 5 are:
- x = √5 - 3
- x = -√5 - 3
These are the exact solutions. If you need an approximate decimal representation, you can use a calculator to evaluate these expressions.