use the quadratic equation x^2-22x=75 to answer the following questions
Part B: Rewrite the equation in the form (x-h)^2+k=0
Part C: Solve the quadratic equation to find the positive solution for x
Part D: Solve the quadratic equation to find the negative solution for x
Part B: To rewrite the equation x^2 - 22x = 75 in the form (x-h)^2 + k = 0, we need to complete the square.
First, add (22/2)^2 = 121 to both sides of the equation:
x^2 - 22x + 121 = 75 + 121
x^2 - 22x + 121 = 196
Next, rewrite the left side as a perfect square:
(x - 11)^2 = 196
So, the equation in the form (x-h)^2 + k = 0 is:
(x - 11)^2 - 196 = 0
Part C: To solve the quadratic equation (x - 11)^2 - 196 = 0 for the positive solution of x, we need to isolate x:
(x - 11)^2 = 196
(x - 11) = ±√196
(x - 11) = ±14
Now, solve for x:
x = 11 + 14
x = 25
Therefore, the positive solution for x is x = 25.
Part D: To solve the quadratic equation (x - 11)^2 - 196 = 0 for the negative solution of x, we follow the same steps as in Part C:
(x - 11)^2 = 196
(x - 11) = ±√196
(x - 11) = ±14
Now, solve for x:
x = 11 - 14
x = -3
Therefore, the negative solution for x is x = -3.