Question
Find all real solutions of the equation. (Enter your answers as a comma-separated list.) \[ 4 x^{2}-100=0 \] Need Help? Read it SUBMIT ANSWER
Ask by Mccoy Norton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The real solutions are 5, -5.
Solution
To solve the equation \( 4x^{2} - 100 = 0 \):
1. **Add 100 to both sides**:
\[
4x^{2} = 100
\]
2. **Divide both sides by 4**:
\[
x^{2} = 25
\]
3. **Take the square root of both sides**:
\[
x = \sqrt{25} \quad \text{or} \quad x = -\sqrt{25}
\]
\[
x = 5 \quad \text{or} \quad x = -5
\]
**So, the real solutions are:**
**5, -5**
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Simplify this solution The Deep Dive
To solve the equation \( 4x^{2} - 100 = 0 \), first, you can add 100 to both sides: \[ 4x^{2} = 100 \] Next, divide both sides by 4: \[ x^{2} = 25 \] Now, take the square root of both sides. Remember, taking the square root gives both positive and negative solutions: \[ x = 5 \quad \text{or} \quad x = -5 \] So, the real solutions of the equation are: \[ 5, -5 \]
