I'm having trouble in my hs pre calc class

Question

I'm confused on how to solve and simplify. for example x^2-6x +4=0

Answer 1

Here's a good site: http://www.purplemath.com/modules/solvquad.htm

 

But, just a quick explanation.

 

1)The coefficient in front of the term that is square is A.

2)The coefficient in front of the x term is B.

3) The term that is added or subtracted from this is C.

 

In this case, A=1, B=-6, and C=4

 

To solve, you need to fill in the blanks in this expression: (x+__)(x+__).

 

What you're looking for is factors of C that add up to B; each factor fills in a blank.

In this case, the expression does not factor without using the quadratic equation, so let's look at a basic one that does.

 

x²+2x-15=0

 

A=1, B=2, C=-15.

 

So, we need to find factors of -15 that will add up to 2, or in other words, two numbers that multiply to make -15.

 

Let's try 1 and 15. 1 times 15 equals 15, but no matter how you add 1, -1, 15, or -15, you can't make 2.

What about 3 and 5? 3 times 5 equals 15. Can we make 2 by adding 5 and 3? Yep! If you have a a positive 5 and a negative 3, you can get 2: 5-3=2. We have found our answer.

 

(x+5)(x-3)=0

 

If you multiply two things together, and get zero, one of them must be zero. So x+5=0 or x-3=0, which means the solutions to this, or the factors, are 3 and -5. If you want to check your answer, put 3 or -5 in the original equation, or FOIL the two factors. 

 

I hope that made sense!

Answer 2

x² - 6x + 4 = 0

 

Use the quadratic formula:

 

x = -(b/2a) ± (1/2a)√(b²-4*a*c)

 

Where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.  For this problem, a=1, b=-6, c=4;

 

x = -(-6)/2*1 ± (1/2)√((-6)²-4*1*4))

 

x = 3 ± (√20)/2

 

x = 3 ± √5