Question
Question Use the square roots property to solve the quadratic equation \( u^{2}-270=-266 \). If there are multiple answers, list them separated by a comma, e.g. 1,2 . If there is no real solution, enter \( \varnothing \).
Ask by Salazar Floyd. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are: 2, -2.
Solution
We start with the equation:
u² - 270 = -266
Step 1: Add 270 to both sides:
u² = -266 + 270
u² = 4
Step 2: Take the square root of both sides (don’t forget the ±):
u = √4 or u = -√4
u = 2 or u = -2
Thus, the solutions are: 2, -2.
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Simplify this solution Bonus Knowledge
First, we can rewrite the equation \( u^{2}-270=-266 \) as \( u^{2}=270-266 \), which simplifies to \( u^{2}=4 \). Now, applying the square roots property gives us \( u = \sqrt{4} \) or \( u = -\sqrt{4} \). Thus, the solutions are \( u = 2 \) and \( u = -2 \). The answers are: 2, -2.
