Final answer:
To find the solutions of the equation x² = 6, take the positive and negative square roots of 6, resulting in two solutions: x = √6 and x = -√6, which approximate to x ≈ 2.4495 and x ≈ -2.4495 respectively.
Step-by-step explanation:
The solutions of the equation x² = 6 can be found by taking the square root of both sides. Because the square of a number can be positive or negative, we consider both the positive and negative square roots.
To solve for x, we perform the following steps:
- Take the square root of both sides: √x² = √6
- Solve for x: x = ±6√6
This means that the equation x² = 6 has two solutions: x = √6 and x = -√6.
The value √6 is approximately 2.4495, so the approximate solutions are x ≈ 2.4495 and x ≈ -2.4495.