SOLUTION: Solve the equation and check your solutions. (x-1)(x^2+10x+24)=0 This is what I have tried x-1=0 x=1 x^2+10x+24=0 x^2 +10x-6-4

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Question 273284: Solve the equation and check your solutions.
(x-1)(x^2+10x+24)=0
This is what I have tried
x-1=0
x=1
x^2+10x+24=0
x^2 +10x-6-4

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
You have the first solution of , you just need to solve

So let's solve by use of the quadratic formula.

Solved by pluggable solver: Quadratic Formula

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=10, and c=24

Square 10 to get 100

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

So the next two solutions are and

This means that the three solutions are , and

I'll let you check the solutions.