SOLUTION: please can you show me a method of how to work out this equation x^2+9x+14=0

Question 122834: please can you show me a method of how to work out this equation x^2+9x+14=0
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=9, and c=14

Square 9 to get 81

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:
You can always solve a quadratic equation using the quadratic formula:
and, of course, the a, b, and c come from the standard form of the equation:

So, in this case, a = 1, b = 9, and c = 14
Making the appropriate substitutions into the quadratic formula, we get:

or
or
If the given trinomial can be factored, this offers another way to solve the problem:
Factor the trinomial.
Apply the zero product principle.
or , then...
If then
If then
So in both cases, you get the same solutions:

A third way would be to graph the equation () and identify the x-intercepts (also called "the zeros").

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