solve. w²-9w+14=0 (solution is/are w= ____) type an integer or a simple fraction, use comma to separate answers as needed,type each solution only once.
"Solution" means a number that you could put in place of 'w' and the
equation would be a true statement.
Since 'w' appears to the second power in the equation, you expect 2 solutions.
You almost always have to start out by factoring the left side:
w² - 9w + 14 = 0
I hope you know how to factor a quadratic expression, because it's
too complicated to explain in a few sentences.
In factored form, this one is
(w - 7) times (w - 2) = 0
The important key point here is that this factored form is zero
if either factor is zero. That leads you to the two solutions.
w - 7 = 0
w = 7
w - 2 = 0
w = 2
There are your two solutions. If you put either 7 or 2 in place
of 'w' in the original equation, then the left side is equal to zero.
No other number will do that. The solutions are w=7 and w=2.
[latex]w^2-9w+14=0 \\ \\w^2-7w-2w+14=0 \\ \\ w(w-7)-2(w-7)=0\\ \\(w-7)(w-2)=0 \\ \\w-7 =0 \ \ \ or \ \ \ w-2 = 0\\ \\ w=7 \ \ \ or \ \ \ w = 2[/latex]