Pregunta
22. Higher Order Thinking a. Solve \( (x-5)^{2}-100=0 \). Show the steps for yoution.
Ask by Lindsey Clarke. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solutions are \( x = 15 \) and \( x = -5 \).
Solución
1. Start with the equation:
\[
(x-5)^2 - 100 = 0
\]
2. Add \(100\) to both sides:
\[
(x-5)^2 = 100
\]
3. Take the square root of both sides (remembering to consider both positive and negative roots):
\[
x-5 = \pm \sqrt{100}
\]
\[
x-5 = \pm 10
\]
4. Solve for \(x\) for each case:
- If \(x-5 = 10\):
\[
x = 10 + 5 = 15
\]
- If \(x-5 = -10\):
\[
x = -10 + 5 = -5
\]
5. The solutions are:
\[
x = 15 \quad \text{or} \quad x = -5
\]
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Simplifique esta solución The Deep Dive
To solve the equation \( (x-5)^{2}-100=0 \), start by isolating the squared term. Add 100 to both sides to get \( (x-5)^{2}=100 \). Then, take the square root of both sides: \( x-5 = \pm 10 \). This gives us two equations: \( x-5=10 \) and \( x-5=-10 \). Solving these, we find \( x=15 \) and \( x=-5 \). So the solutions are \( x=15 \) and \( x=-5 \). Understanding the process behind higher-order thinking in mathematics allows for deeper problem-solving strategies. For instance, relating similar problems and recognizing patterns in equations can enhance your ability to tackle more complex challenges in algebra and beyond!
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