Question
Identify the first step when solving for x in the following equation. \( \sqrt{4 x}=x-2 \) Divide by 4 on both sides. Square both sides. Subtract x from both sides. Add 2 to both sides.
Ask by Schultz Huff. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The first step is to square both sides.
Solution
The first step is to eliminate the square root by squaring both sides.
Starting with
\[
\sqrt{4x} = x-2,
\]
we square both sides to obtain
\[
(\sqrt{4x})^2 = (x-2)^2.
\]
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Simplify this solution Extra Insights
The first step to solving \( \sqrt{4 x} = x - 2 \) is to square both sides. This eliminates the square root, giving you \( 4x = (x - 2)^2 \). Just remember, squaring both sides might introduce extraneous solutions, so you'll want to check your answers at the end! Once you have squared both sides, you can expand the right-hand side to get \( 4x = x^2 - 4x + 4 \). Then, tantalizingly combine like terms to form a quadratic equation, which is always a fun challenge! Keep those mathematical gears turning!
