Bot GPT 4-o mini To determine whether the values \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rewrite the equation in standard form by subtracting 3 from both sides:
\[ 3x^2 - 4x - 4 - 3 = 0 \] \[ 3x^2 - 4x - 7 = 0 \]
Now we can check each value separately by substituting them into the equation \( 3x^2 - 4x - 7 \) and seeing if the result equals zero.
1. Check \( x = -1 \):
\[ 3(-1)^2 - 4(-1) - 7 \]
Calculating this step-by-step:
\[ 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \]
So, \( x = -1 \) is a solution.
2. Check \( x = 73 \):
\[ 3(73)^2 - 4(73) - 7 \]
Calculating this step-by-step:
\[ 3(5329) - 292 - 7 = 15987 - 292 - 7 = 15987 - 299 = 15688 \]
Since \( 15688 \neq 0 \), \( x = 73 \) is not a solution.
Based on our checks:
- \( x = -1 \) is a solution.
- \( x = 73 \) is not a solution.
Thus the correct response is:
Only \( x = -1 \) is a solution.
1 answer