x^2-5x=-10 =x=5+i sqrt15/2 ,5-i sqrt15/2.
CAN SOMEONE CHECK MY ANSWER.
Correct.
Thank you for looking at my work.
To check the answer for the equation x^2 - 5x = -10, we need to substitute the calculated values into the equation and see if it holds true.
The given solutions you provided are x = 5 + i√15/2 and x = 5 - i√15/2. Let's check these solutions:
Substituting the first solution, x = 5 + i√15/2:
(5 + i√15/2)^2 - 5(5 + i√15/2) = -10
Expanding the square:
(25 + 2i√15 + (i√15/2)^2) - 25 - 5i√15 - 10 = -10
Simplifying the equation:
25 + 2i√15 - 15/4 - 25 - 5i√15 - 10 = -10
Combining like terms:
-15/4 - 10 = -10 - 25 - 2i√15 - 5i√15
Simplifying further:
-55/4 = -35 - 7i√15
As the left-hand side (-55/4) is not equal to the right-hand side (-35 - 7i√15), the first solution, x = 5 + i√15/2, is not correct.
Now, let's check the second solution, x = 5 - i√15/2:
(5 - i√15/2)^2 - 5(5 - i√15/2) = -10
Expanding the square:
(25 - 2i√15 + (i√15/2)^2) - 25 + 5i√15 - 10 = -10
Simplifying the equation:
25 - 2i√15 - 15/4 - 25 + 5i√15 - 10 = -10
Combining like terms:
-15/4 - 10 = -10 + 25 - 2i√15 + 5i√15
Simplifying further:
-55/4 = 15 + 3i√15
As the left-hand side (-55/4) is not equal to the right-hand side (15 + 3i√15), the second solution, x = 5 - i√15/2, is also not correct.
In conclusion, the given solutions x = 5 + i√15/2 and x = 5 - i√15/2 do not satisfy the equation x^2 - 5x = -10. Therefore, they are not the correct solutions.