Question

Solve the equation by completing the square.

x^2+9x-14=0

Answer 1

x=7 or 2

Answer 2

The answer choices are
A. 10.35, 1.35
B. 10.35, -1.35
C. -10.35, -1.35
D. -10.35, 1.35

Answer 3

Completing the square calls for you to not only factor the equation, but make it so that the factor is the same (x+2)^2 for example, rather than (x-1)(x+4) or 2 other different parenthesis.
So x^2 + 9x + ? = 0
If 9x is positive, and they have to be the same sign, then the '?' would have to be 2 * ? = 9
Thus, the missing number is 4.5
So what number would you have to have in order to get 4.5?
Well, you'd square 4.5, which is 20.25
Thus, you have to have x^2+9x+20.25 in order to complete the square. However, this added 20.25 didn't come from nowhere! You have to add 20.25 to BOTH sides of the equation. Before you do this, however, you should add 14 to both sides. You now have: \[x^2+9x+20.25=14+20.25\]
Factored is:
\[(x+4.5)^2=34.25\]
Square root both sides and you have \[x+4.5=\sqrt34.25\]
Subtract 4.5 from both sides and you have:
\[x=\sqrt34.25 - 4.5\]
Remember when you square root something, the answer can be negative or positive!
Thus, x=5.85-4.5
and x=-5.85-4.5
Which means that x=1.35 and x=-10.35

Answer 4

Thank you so much!!!