Question
Question Use the square roots property to solve the quadratic equation \( 4 a^{2}=36 \). 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 Bradley Campbell. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are 3 and -3.
Solution
Start with the equation:
4a² = 36
Divide both sides by 4:
a² = 9
Now apply the square root property:
a = √9 and a = –√9
Since √9 = 3, the solutions are:
a = 3, a = –3
Therefore, the answer is 3, -3.
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Simplify this solution The Deep Dive
To solve the equation \( 4a^2 = 36 \), first, divide both sides by 4 to simplify it: \( a^2 = 9 \). Next, apply the square roots property, which tells us that if \( a^2 = b \), then \( a = \pm\sqrt{b} \). Here, \( b = 9 \). Thus, \( a = \pm\sqrt{9} = \pm3 \). The solutions are \( 3, -3 \).
