Question

Solve the quadratic equation algebraically x2 - 2x − 2 = 1

Answer 1

Answer:

Factoring x2-2x-3

The first term is, x2 its coefficient is 1 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .

-3 + 1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1

x2 - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(x+1) • (x-3)

Which is the desired factorization

Answer 2

Answer:

=> x² - 2x - 2 = 1

=> x² - 2x - 3 = 0

=> x² + x - 3x - 3 = 0

=> x(x + 1) - 3(x + 1) = 0

=> (x - 3)(x + 1) = 0

=> x - 3 = 0 or x + 1 = 0

So, x = 3 or x = -1