Question
Create a function graph to answer the question. Use the function graph to solve for the solutions to the equation x2+2x=3
.(1 point)
Responses
x=0,1
x equals 0 comma 1
x=−3,1
x equals negative 3 comma 1
x=2,0
x equals 2 comma 0
no solution
.(1 point)
Responses
x=0,1
x equals 0 comma 1
x=−3,1
x equals negative 3 comma 1
x=2,0
x equals 2 comma 0
no solution
Answers
GPT-4o mini
To solve the equation \( x^2 + 2x = 3 \), we first rewrite it in standard form:
\[ x^2 + 2x - 3 = 0 \]
Next, we can factor the quadratic equation:
\[ (x + 3)(x - 1) = 0 \]
Setting each factor equal to zero gives us the potential solutions:
1. \( x + 3 = 0 \) ⟹ \( x = -3 \)
2. \( x - 1 = 0 \) ⟹ \( x = 1 \)
Thus, the solutions are:
- \( x = -3 \)
- \( x = 1 \)
Now, matching this with your provided responses, we have:
**Response**: \( x = -3, 1 \)
So the correct answer is:
- **x equals negative 3 comma 1**
\[ x^2 + 2x - 3 = 0 \]
Next, we can factor the quadratic equation:
\[ (x + 3)(x - 1) = 0 \]
Setting each factor equal to zero gives us the potential solutions:
1. \( x + 3 = 0 \) ⟹ \( x = -3 \)
2. \( x - 1 = 0 \) ⟹ \( x = 1 \)
Thus, the solutions are:
- \( x = -3 \)
- \( x = 1 \)
Now, matching this with your provided responses, we have:
**Response**: \( x = -3, 1 \)
So the correct answer is:
- **x equals negative 3 comma 1**