Final answer:
To solve the quadratic equation x² + 12x + 20 = 0, you can use completing the square or the quadratic formula, resulting in two solutions for x.
Step-by-step explanation:
The student has provided an equation that needs to be solved by completing the square or using another method such as the quadratic formula. The equation given appears to be x² + 12x + 20 = 0, but has some typos.
Assuming the correct equation is x² + 12x + 20 = 0, this is a quadratic equation of the form ax² + bx + c = 0 where a = 1, b = 12, and c = 20.
To solve this quadratic equation, we can factor it directly, complete the square, or apply the quadratic formula which is x = (-b ± √(b² - 4ac)) / (2a).
To complete the square, we aim to transform the quadratic equation into a perfect square trinomial. This involves finding a value that, when added and subtracted to the equation, allows us to express it as (x + k)² = m for some values of k and m. We can then take the square root of both sides and solve for x.
Alternatively, the quadratic formula provides a straightforward solution as follows:
Plugging these values into the quadratic formula, we get:
x = –(12) ± √((12)² – 4(1)(20)) / (2(1))
x = –(12) ± √(144 – 80) / 2
x = –(12) ± √(64) / 2
x = –(12) ± 8 / 2
x = –(12) ± 4
The solutions to the equation x² + 12x + 20 = 0 are thus x = –(6) ± 4. i.e., x= -2 or x= -10