Determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3
To determine if a value is a solution to a quadratic equation, you need to substitute the value into the equation and check if the equation is true.
For the equation 3x^2 - 4x - 4 = 3,
Substituting x = -1:
3(-1)^2 - 4(-1) - 4 = 3
3 + 4 - 4 = 3
3 = 3
The equation is true when x = -1.
Substituting x = 7/3:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - 28/3 - 36/3 = 3
147/9 - 64/3 - 108/9 = 3
147/9 - 192/9 - 108/9 = 3
(147 - 192 - 108)/9 = 3
-153/9 = 3
-17 = 3
The equation is not true when x = 7/3.
Therefore, the value -1 is a solution to the quadratic equation, but 7/3 is not.
To determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3, we substitute the values into the equation and check if they make the equation true.
1. For x = -1:
Plug in x = -1 into the equation: 3(-1)^2 - 4(-1) - 4 = 3
Simplify: 3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
The equation holds true when x = -1.
2. For x = 7/3:
Plug in x = 7/3 into the equation: 3(7/3)^2 - 4(7/3) - 4 = 3
Simplify: 3(49/9) - (28/3) - 4 = 3
49/3 - 28/3 - 4 = 3
49/3 - 28/3 - 12/3 = 3
(49 - 28 - 12)/3 = 3
9/3 = 3
3 = 3
The equation also holds true when x = 7/3.
Therefore, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.
To determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3, we need to substitute each value into the equation and check if the equation holds true.
Let's start with -1. Substitute -1 for x in the equation:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
Since both sides of the equation are equal, -1 is a solution to the quadratic equation.
Now let's move on to 7/3. Substitute 7/3 for x in the equation:
3(7/3)^2 - 4(7/3) - 4 = 3
3(49/9) - 28/3 - 4 = 3
147/9 - 84/9 - 4 = 3
(147 - 84 - 36)/9 = 3
27/9 = 3
3 = 3
Again, both sides of the equation are equal, so 7/3 is also a solution to the quadratic equation.
In conclusion, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.