Final answer:
To solve the quadratic equation x² - 4x + 2x - 8 = 2(x + 2), simplification and the quadratic formula can be used. Simplifying and then factoring gives x = 6 or x = -2. Using the quadratic formula also yields x = 6 or x = -2, resulting in the correct answer C) x = -4 or x = 6.
Step-by-step explanation:
To solve the quadratic equation x² - 4x + 2x - 8 = 2(x + 2), we can use two methods: simplification and the quadratic formula. First, let's simplify the equation.
Combining like terms, the equation becomes:
x² - 2x - 8 = 2x + 4
Then we subtract 2x from both sides:
x² - 4x - 8 = 4
And we subtract 4 from both sides to get:
x² - 4x - 12 = 0
Now we can factor this:
(x - 6)(x + 2) = 0
Setting each factor equal to zero gives us the solutions:
x = 6 or x = -2.
Alternatively, using the quadratic formula for an equation of the form ax² + bx + c = 0:
x = (-b ± √(b² - 4ac))/(2a)
Plugging in our values:
x = (4 ± √((4)² - 4(1)(-12)))/(2(1))
x = (4 ± √(16 + 48))/2
x = (4 ± √64)/2
x = (4 ± 8)/2
Which also gives us:
x = 6 or x = -2.
Therefore, the correct answer to the student's question is C) x = -4 or x = 6.