Question

Solve for all values of x by factoring. x²-11x+22=-2

Answer 1

Step-by-step explanation:

1. add 2 ---
2. 
   `{x}^(2) - 11x + 24 = 0`
3. find two numbers that both multiply to make 24 and add up to -11x. in this case the numbers would be -8 and -3. this is because when added up they make -11x if you multiply them they make positive 24.
4. put the numbers in brackets along with the x
5. 
   `(x - 3)(x - 8) = 0`
6. you will have two solutions. to get the answer you look at the brackets as separate equations and solve them both so

1. 
   `x - 3 = 0 \\ + 3 \\ x = 3`
2. 
   `x - 8 \\ + 8 \\ x = 8`
3. these are your answers

Answer 2

To solve the equation x^2-11x+22=-2, we rewrite it as x^2-11x+24=0 and factor it into (x-8)(x-3)=0. The solutions are x=8 and x=3.

Step-by-step explanation:

To solve the equation x²-11x+22=-2 by factoring, we first need to move all terms to one side of the equation to set it equal to zero. This gives us x²-11x+24=0. Now, we look for two numbers that multiply to 24 and add to -11. These numbers are -8 and -3, as they satisfy both conditions: (-8)(-3) = 24 and (-8) + (-3) = -11.

Using these numbers, we can factor the quadratic equation as follows:

(x - 8)(x - 3) = 0

Now, we set each factor equal to zero and solve for x:

• x - 8 = 0 → x = 8
• x - 3 = 0 → x = 3

Thus, the solution to the equation by factoring is x = 8 or x = 3.