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Solving the Equation (x + 15)² = 6
This equation involves a squared term, which means we need to use the square root property to solve for x. Here's how:
1. Isolate the Squared Term
Begin by isolating the squared term on one side of the equation. In this case, it's already isolated:
(x + 15)² = 6
2. Take the Square Root of Both Sides
Take the square root of both sides of the equation. Remember that taking the square root results in both positive and negative solutions:
√(x + 15)² = ±√6
This simplifies to:
x + 15 = ±√6
3. Solve for x
Now, isolate x by subtracting 15 from both sides:
x = -15 ±√6
4. Simplify the Solution
We now have two possible solutions:
- x = -15 + √6
- x = -15 - √6
These are the exact solutions. You can approximate them to decimal form if needed.
Therefore, the solutions to the equation (x + 15)² = 6 are x = -15 + √6 and x = -15 - √6.