Solve the following equation.
x squared minus 3 x minus 8 equals x plus 4
(1 point)
Responses
x equals negative 6 or x = 2
Image with alt text: x equals negative 6 or x = 2
x equals 1 plus Start Root 5 End Root or x equals 1 minus Start Root 5 End Root
Image with alt text: x equals 1 plus Start Root 5 End Root or Image with alt text: x equals 1 minus Start Root 5 End Root
x equals 1 plus 2 Start Root 3 End Root or x equals 1 minus 2 Start Root 3 End Root
Image with alt text: x equals 1 plus 2 Start Root 3 End Root or Image with alt text: x equals 1 minus 2 Start Root 3 End Root
x equals negative 2 or x = 6
The correct answer is:
x equals negative 2 or x = 6
To solve the equation "x squared minus 3x minus 8 equals x plus 4," we can first rearrange the terms to get:
x^2 - 3x - 8 = x + 4.
Next, we can bring all the terms to one side of the equation:
x^2 - 3x - x - 8 - 4 = 0.
Simplifying further:
x^2 - 4x - 12 = 0.
Now, we'll factor the quadratic equation:
(x - 6)(x + 2) = 0.
To find the values of x, we set each factor equal to zero:
x - 6 = 0 or x + 2 = 0.
Solving for x:
If x - 6 = 0, then x = 6.
If x + 2 = 0, then x = -2.
Therefore, the solutions to the equation are x = 6 and x = -2.