Pre algebra
posted by Grace
How do I solve Quadratic equations by factoring?
(for example how would I solve n2  10n = 21 if I was supposed to get the answers 7 and 3?

Steve
first, set everything equal to zero.
n^2  10n + 21 = 0
now, since (na)(nb) = n^2  (a+b)n + ab, we are looking for two numbers a and b, which multiply to 21 and add to 10.
Now, the only factor of 21 are 7 and 3. Luckily, they add to 10, so we have
(n7)(n3) = n^2  10n + 21
Now, back to step 1. Why set everything to zero? We now have
(n7)(n3) = 0
the only way two numbers can multiply to zero is if one or the other of them is zero. So, we have either
n7 = 0 ==> n=7
or
n3 = 0 ==> n=3
Those are the solutions to
(n7)(n3) = 0, which is just a rewriting of the original equation.
Respond to this Question
Similar Questions

8th Grade Algebra
You know how to solve quadratic equations using algebra, graphs and the quadratic formula. Sometimes one method of solving is more convenient than another method. Describe how you would solve each equation. Give reasons for you answers. … 
algebra 2
how do you solve quadratic equations by factoring? 
Math (Algebra) Repost from July 27, 2010 at 4:13pm
Could someone help to explain to me how factoring is used to solve quadratic equations? 
Math
Explain how factoring is used to solve quadratic equations. Demonstrate the process with an example. 
ALGEBRA
Explain how factoring is used to solve quadratic equations. Demonstrate the process with an example. 
math
please anwer these: 1) how can i multiply and divide polynomials containing radicals? 
math
Jenny wanted to solve the quadratic equation x2  11x +18 = 0 by factoring. Which of the following equations would lead her to solve the given equation? 
Algebra
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula. (Enter your answers as a commaseparated list.) … 
Algebra
Factor quadratic expressions: 2x^2 + 9x + 4 10x^2 + 70x + 100 Solve quadratic equations by factoring: 2x^2 + 9x + 4 = 0 Solve by taking square roots: (x  5)^2  81 = 0 
Algebra II
Need help please. Thank you. 1. Determine whether the function has a maximum or minimum. State that value. f(x)= 2x^24x 2. Determine what c would in order to complete the square. x^25x+c 3. Solve the quadratic by factoring. 3x^216x+5=0 …