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Solving the Equation (x+15)^2 = 54
This article will guide you through solving the equation (x+15)^2 = 54. We'll break down each step, ensuring clarity and understanding.
1. Isolate the Squared Term
First, we need to isolate the term that's being squared. To do this, we take the square root of both sides of the equation:
√((x+15)^2) = √54
This simplifies to:
x + 15 = ±√54
Note: We include the ± symbol because both the positive and negative square roots of 54 will satisfy the equation.
2. Simplify the Square Root
Next, we simplify the square root of 54:
√54 = √(9 * 6) = 3√6
3. Solve for x
Now we have:
x + 15 = ±3√6
To isolate 'x', subtract 15 from both sides:
x = -15 ± 3√6
4. The Solution
Therefore, the solutions to the equation (x+15)^2 = 54 are:
- x = -15 + 3√6
- x = -15 - 3√6
These are the two possible values of 'x' that satisfy the original equation.