Question
\( 50 x^{2}=70 \) What is one of the solutions to the given equation?
Ask by Robbins Todd. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
One solution is \( x = \frac{\sqrt{35}}{5} \).
Solution
Solve the equation \( 50x^{2}=70 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(50x^{2}=70\)
- step1: Divide both sides:
\(\frac{50x^{2}}{50}=\frac{70}{50}\)
- step2: Divide the numbers:
\(x^{2}=\frac{7}{5}\)
- step3: Simplify the expression:
\(x=\pm \sqrt{\frac{7}{5}}\)
- step4: Simplify the expression:
\(x=\pm \frac{\sqrt{35}}{5}\)
- step5: Separate into possible cases:
\(\begin{align}&x=\frac{\sqrt{35}}{5}\\&x=-\frac{\sqrt{35}}{5}\end{align}\)
- step6: Rewrite:
\(x_{1}=-\frac{\sqrt{35}}{5},x_{2}=\frac{\sqrt{35}}{5}\)
The solutions to the equation \(50x^{2}=70\) are \(x_{1}=-\frac{\sqrt{35}}{5}\) and \(x_{2}=\frac{\sqrt{35}}{5}\).
Therefore, one of the solutions to the given equation is \(x_{2}=\frac{\sqrt{35}}{5}\).
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Simplify this solution Extra Insights
To solve the equation \( 50 x^{2} = 70 \), you first divide both sides by 50, leading to \( x^{2} = \frac{70}{50} = 1.4 \). Taking the square root of both sides gives \( x = \pm \sqrt{1.4} \). One of the solutions is approximately \( x \approx 1.183 \). Finding solutions like this can show you the elegance of algebra! Imagine you're one step closer to solving practical problems, whether it's calculating areas or optimizing designs. That’s math finding its place in the real world!
