Pre algebra

posted by .

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?

• Pre algebra -

first, set everything equal to zero.

n^2 - 10n + 21 = 0

now, since (n-a)(n-b) = 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

(n-7)(n-3) = n^2 - 10n + 21

Now, back to step 1. Why set everything to zero? We now have

(n-7)(n-3) = 0

the only way two numbers can multiply to zero is if one or the other of them is zero. So, we have either

n-7 = 0 ==> n=7
or
n-3 = 0 ==> n=3

Those are the solutions to
(n-7)(n-3) = 0, which is just a rewriting of the original equation.

Similar Questions

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. …
2. algebra 2

how do you solve quadratic equations by factoring?
3. 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?
4. Math

Explain how factoring is used to solve quadratic equations. Demonstrate the process with an example.
5. ALGEBRA

Explain how factoring is used to solve quadratic equations. Demonstrate the process with an example.
6. math

please anwer these: 1) how can i multiply and divide polynomials containing radicals?
7. 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?
8. 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 comma-separated list.) …
9. 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
10. Algebra II

Need help please. Thank you. 1. Determine whether the function has a maximum or minimum. State that value. f(x)= -2x^2-4x 2. Determine what c would in order to complete the square. x^2-5x+c 3. Solve the quadratic by factoring. 3x^2-16x+5=0 …

More Similar Questions