solve x squared +6x+8=0

Question

solve x squared +6x+8=0

Answer 1

Hi there, Gayla,

What you want to do is find two factors that when multiplied give the original.

Start out with (x  )(x  )=0

The + in front of the constant term tells us that both symbols will be the same, and the + in front of the 6x tells us they will both be positive:

Start out with (x +)(x + )=0

Now we are looking for two numbers that multiply to 8 and add to 6.  What about 2 and 4?  Yes!  That works.

Start out with (x + 2)(x + 4)=0

If either one of the factors equals 0, then the product will be 0, so either

(x + 2)=0 or (x + 4)=0

So x = -2 or -4

Hope that explanation helps!

Debbie

Answer 2

Hi Gayla.

There are 2 ways you can solve this problem.  The first way is to factor the expression x²+6x+8 into the form (x+u)(x+z).  If you multiply (x+u) and (x+z), you will get x²+(u+z)+u*z.  Therefore,

x²+(u+z)+u*z = x²+6x+8

By comparing the two sides, we can see that u+z = 6 and u*z = 8.  This is a system of two equations, which we can solve to find u and z.  Or you can simply guess and check and you will find that u and z are equal to 2 and 4 (since 2+4 = 6 and 2*4 = 8).  Now the equation looks like this:

(x+2)(x+4)=0

Now it's easy to find the values of x, because x is any number that causes one of the factors to be equal to zero.  If x+2=0, then x=-2.  In the same way, if x+4=0, then x=-4

So the solutions are x = -2,-4

 

The second way is to recognize that this is a quadratic equation, which means you can use the quadratic equation:

x = [-b+sqrt(b²-4*a*c)]/2a

or

x = [-b-sqrt(b²-4*a*c)]/2a

In this problem, a=1, b=6, and c=8.  You can plug these values into the quadratic equation, and you will get the same answers: x = -2,-4