%5E2%3D54-square-root.jpeg "(x+15)^2=54 Square Root")
Solving the Equation (x + 15)² = 54
This equation involves a square and requires us to use the square root to solve for x. Let's break down the steps:
1. Isolate the Squared Term
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Begin by taking the square root of both sides of the equation. Remember that taking the square root can result in both positive and negative solutions.
√(x + 15)² = ±√54
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This simplifies to:
x + 15 = ±√54
2. Simplify the Radical
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Find the prime factorization of 54: 54 = 2 × 3 × 3 × 3 = 2 × 3² × 3.
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We can take the square root of 3² which is 3:
x + 15 = ±√(2 × 3² × 3) = ±3√6
3. Isolate x
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Subtract 15 from both sides of the equation:
x = -15 ± 3√6
4. The Solutions
Therefore, the solutions to the equation (x + 15)² = 54 are:
- x = -15 + 3√6
- x = -15 - 3√6
These are the exact solutions. You can approximate them using a calculator if needed.