SOLUTION: I am having some difficulty with quadratic equations. The problem is, I don't understand the steps I should take to get the correct answer. Could you possibly show me each step I s

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I am having some difficulty with quadratic equations. The problem is, I don't understand the steps I should take to get the correct answer. Could you possibly show me each step I s      Log On


   

Question 361402: I am having some difficulty with quadratic equations. The problem is, I don't understand the steps I should take to get the correct answer. Could you possibly show me each step I should take to find the anwer? I appreciate anyone and everyone's help!
Section 11.4, #6
Direction: Solve the equation by making an appropriate substitution.
(2x-4 )^2-6(2x-4)-7=0 (it should say (2x-4) squared)
The correct answer according to the book is: {3/2. 11/2}
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-4+%29%5E2-6%282x-4%29-7=0 Start with the given equation.


4x%5E2-16x%2B16-6%282x-4%29-7=0 FOIL


4x%5E2-16x%2B16-12x%2B24-7=0 Distribute.


4x%5E2-28x%2B33=0 Combine like terms.


Now let's solve the equation using the quadratic formula.


For more help with the Quadratic Formula, check out this solver

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 4%2Ax%5E2-28%2Ax%2B33=0 ( notice a=4, b=-28, and c=33)





x+=+%28--28+%2B-+sqrt%28+%28-28%29%5E2-4%2A4%2A33+%29%29%2F%282%2A4%29 Plug in a=4, b=-28, and c=33




x+=+%2828+%2B-+sqrt%28+%28-28%29%5E2-4%2A4%2A33+%29%29%2F%282%2A4%29 Negate -28 to get 28




x+=+%2828+%2B-+sqrt%28+784-4%2A4%2A33+%29%29%2F%282%2A4%29 Square -28 to get 784 (note: remember when you square -28, you must square the negative as well. This is because %28-28%29%5E2=-28%2A-28=784.)




x+=+%2828+%2B-+sqrt%28+784%2B-528+%29%29%2F%282%2A4%29 Multiply -4%2A33%2A4 to get -528




x+=+%2828+%2B-+sqrt%28+256+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%2828+%2B-+16%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2828+%2B-+16%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%2828+%2B+16%29%2F8 or x+=+%2828+-+16%29%2F8


Lets look at the first part:


x=%2828+%2B+16%29%2F8


x=44%2F8 Add the terms in the numerator

x=11%2F2 Divide


So one answer is

x=11%2F2




Now lets look at the second part:


x=%2828+-+16%29%2F8


x=12%2F8 Subtract the terms in the numerator

x=3%2F2 Divide


So another answer is

x=3%2F2


So our solutions are:

x=11%2F2 or x=3%2F2