Question
What are the two solutions to the equation below? \[ \frac{d^{2}}{4}+43=52 \]
Ask by Warren Norris. in Spain
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( d = 6 \) and \( d = -6 \).
Solution
To solve the equation:
\[
\frac{d^{2}}{4} + 43 = 52
\]
follow these steps:
1. **Subtract 43 from both sides** to isolate the term with \( d^2 \):
\[
\frac{d^{2}}{4} = 52 - 43
\]
\[
\frac{d^{2}}{4} = 9
\]
2. **Multiply both sides by 4** to eliminate the denominator:
\[
d^{2} = 9 \times 4
\]
\[
d^{2} = 36
\]
3. **Take the square root of both sides** to solve for \( d \):
\[
d = \pm \sqrt{36}
\]
\[
d = \pm 6
\]
**Solutions:**
\[
d = 6 \quad \text{and} \quad d = -6
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
First, let's simplify the equation. We start with \(\frac{d^{2}}{4} + 43 = 52\). Subtracting 43 from both sides gives us \(\frac{d^{2}}{4} = 9\). Now, we multiply both sides by 4 to eliminate the fraction, leading to \(d^{2} = 36\). Finally, to find \(d\), we take the square root of both sides. This yields \(d = 6\) and \(d = -6\) as the two solutions! To visualize this, think of a number line: both 6 and -6 are equidistant from zero, making them the classic "twins" in the world of equations! Whether you're diving into math for fun or facing a test, knowing how to maneuver through these equations opens up a whole new world of problem-solving possibilities.
