Brooks Colon
05/28/2024 · Elementary School
4. The aquare of a number minus twice the number is fifteen. What are the numbers.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's denote the number as \( x \).
The given information can be represented as an equation:
\[ x^2 - 2x = 15 \]
To find the numbers, we need to solve this quadratic equation. Let's solve it using the quadratic formula.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-2x=15\)
- step1: Move the expression to the left side:
\(x^{2}-2x-15=0\)
- step2: Factor the expression:
\(\left(x-5\right)\left(x+3\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&x-5=0\\&x+3=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=5\\&x=-3\end{align}\)
- step5: Rewrite:
\(x_{1}=-3,x_{2}=5\)
The solutions to the equation \( x^2 - 2x = 15 \) are \( x = -3 \) and \( x = 5 \).
Therefore, the numbers are -3 and 5.
Quick Answer
The numbers are -3 and 5.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit