SOLUTION: How do you solve this quadratic equation??? x squared -17x-9=0

Question 271137: How do you solve this quadratic equation???
x squared -17x-9=0
Found 2 solutions by Greenfinch, Theo:
Answer by Greenfinch(383) (Show Source): You can put this solution on YOUR website!
x^2 - 17x - 9 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=325 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 17.51387818866, -0.513878188659973. Here's your graph:

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is x^2 - 17x - 9 = 0

it cannot be factored without using the quadratic formula or the completing the squares method.

quadratic formula method is:

x = quadratic formula is

equation has to be in standard form of ax^2 + bx + c = 0 which it is.

a = 1
b = -17
c = -9

substitute in quadratic formula to get:

x =

you get:

x = which becomes:

x = which becomes:

x = which becomes:

x = 17.51387819
or
x = -.0513878189

substitute in your original equation to confirm the answers are good.

your original equation is:

x^2 - 17x - 9 = 0

substituting 17.5387819 for x gets 0 = 0 so the first answer is good.

substituting -.5138978189 for x gets 0 = 0 so the second answer is good.

those are your factors.

completing the squares method works as follows:

your original equation is

x^2 - 17x - 9 = 0

add 9 to both sides of the equation to get

x^2 - 17x = 9

take 1/2 of the b term to get:

b/2 = -17/2 = -8.5

square that to get (b/2)^2 = 72.25

your completing the squares formula is:

take the square root of both sides of this equation to get:

= +/-

add 8.5 go both sides of this equation to get:

+/-

solve for x to get:

x = 17.51387819
or

x = -.513878189

they're the same answers you got using the quadratic formula.

you should remember the quadratic formula at least.

anytime you get a quadratic equation that you can't factor easily, use the quadratic formula.

if you prefer to use the completing the squares method, then remember that.

it's a little harder to explain how that works, but it's not too bad to work with once you know how.

you need to remember at least one of them.

the quadratic formula is a formula.

the completing the square method is a method.

i believe the quadratic formula can be derived from the completing the squares method.

while the factoring method only works on quadratic equations when the factors are integers, the quadratic equation and the completing the squares method work on any quadratic equation.

even when the factoring method can be used, it's not always easy to spot the factors, especially when the a term (coefficient of the x^2 term) is not equal to 1.

bottom line is:

don't waste time trying to find the factors using the factoring method unless the question absolutely requires that you solve it that way.

as soon as you are having difficulty finding the factors, revert to the quadratic equation or the completing the squares method, whichever you feel more comfortable with.

here's some references for both the quadratic formula and the completing the squares method.

http://www.purplemath.com/modules/sqrquad.htm
http://www.purplemath.com/modules/quadform.htm
http://www.jamesbrennan.org/algebra/quadratics/the_quadratic_formula.htm

RELATED QUESTIONS
how do you solve this equation? (x-7x)squared=5=0 its a quadratic equation(completing a... (answered by ikdeep)
how do you solve the quadratic equation x squared -9x-10=0 by... (answered by user_dude2008)
how do you solve the quadratic equation 2x squared=... (answered by solver91311)
How do you solve 5x squared plus 16x minus 84 equals 0 using the quadratic equation... (answered by KMST)
how do you solve the quadratic equation 5b squared + 37b -... (answered by solver91311)
how do you solve the quadratic equation m squared- 169=... (answered by solver91311)
How would you solve this quadratic equation 5x squared - 8x... (answered by longjonsilver)
How do I solve and work this quadratic equation?... (answered by Earlsdon)
How do you solve this quadratic equation?... (answered by Edwin McCravy)