To determine which equations can be solved by taking the square root of both sides as the first step, we should identify equations that allow for this operation.
Here are the equations provided:
- \( 9 = 3(x - 2) \)
- \( (x + 5)^2 = 121 \)
- \( x^2 - 49 = 0 \)
- \( x^2 + 10x = 36 \)
Let's analyze each:
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\( 9 = 3(x - 2) \): This is a linear equation. You would typically solve for \( x \) by moving \( 3(x - 2) \) to the other side or simplifying it, not by taking the square root.
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\( (x + 5)^2 = 121 \): This is already in the form of \( A^2 = B \), where you could apply the square root on both sides. So, you can take the square root as the first step.
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\( x^2 - 49 = 0 \): This can be rewritten as \( x^2 = 49 \), which is suitable for taking the square root of both sides. So, this one also allows for it.
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\( x^2 + 10x = 36 \): This equation can be rearranged to \( x^2 + 10x - 36 = 0 \). It's a quadratic equation that would typically be solved using factoring, completing the square, or the quadratic formula, rather than taking the square root directly first.
Based on this analysis, the equations that can be solved by taking the square root of both sides as the first step are:
- \( (x + 5)^2 = 121 \)
- \( x^2 - 49 = 0 \)
So, the answer is the second and third equations.