Equation Problem: x(x-20)=100?

Just did this one

multiply out the bracket

x^2 -20x =100 and rearrange

x^2 -20x -100 =0 then factorise

(x+10) * (x-10) = 0

so x = plus or minus 10

x(x-20)=100

x^2 -10x -10x-100=0

x(x-10) +10(x-10)=0

(x-10)(x+10)=0

x=10 or x=-10

Welcome!

x(x - 20) = 100
x^2 - 20x = 100
x^2 - 20x - 100 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -20
c = -100

x = [20 ±√(400 + 400)]/2
x = [20 ±√800]/2
x = [20 ±√(2^4 * 2 * 5^2)]/2
x = [20 ±(2^2)(5)√2]/2
x = [20 ±20√2]/2
x = 10 ±10√2

∴ x = 10 ±10√2

Edit: try to substitute the answers and see who are right and who are wrong, Shay J.

x² - 20x - 100 = 0
x = [ 20 ± √ (400 + 400 ) ] / 2
x = [ 20 ± √ (800) ] / 2
x = [ 20 ± 10√8 ] / 2
x = [ 20 ± 20√2 ] / 2
x = 10 ± 10√2

x(x - 20) = 100
x^2 - 20x = 100
x^2 - 20x - 100 = 0

x = [-b ± √(b^2 - 4ac)] / 2a

x = [-(-20) + √(-20)^2 - (4 x 1 x -100)] / (2 x 1)
x = (20 + √800) / 2
x = 10 + 10√2
x ≈ 24.14

x = [-(-20) + √(-20)^2 - (4 x 1 x -100)] / (2 x 1)
x = (20 - √800) / 2
x = 10 - 10√2
x ≈ -4.14

Therefore, x = 10 + 10√2 ≈ 24.14 and x = 10 - 10√2 ≈ -4.14

I GUARANTEE that the first two people are WRONG, it is definitely not x = ± 10. It is what sethu said. I just provided the exact answers.

If you put 10 and -10 into the equation you get -100 and 300 respectively, not 100. Oh yeah, screw who ever gave me a 'thumbs down'...stupid people should learn to keep their mouths shut.

the first two answers are correct... the third one uses the quadratic equation but mistakes were made!

a good site for working out problems online is:
http://www.mathway.com

edit: for some reason the "edit" option wasn't here yesterday. i apologized to the original poster as well as to the correct posters who used the quadratic equation. my first answer was incorrect, and if i had used mathway i would have noticed the error. it was late and i made the mistake of trusting the math of the first two posters. anyway... all is well now... the original question has been answered (correctly!).

btw... mr. anderson... i didn't thumbs down you (or anyone here). i will say that if you are a teacher though, you might want to consider getting into some other profession that doesn't involve interacting with people... and thanks for using the site i recommended!

Multiply out:

x^2 - 20x - 100 = 0.

This is of the form ax^2 + bx + c = 0.

Use the formula, we get two values of x:

x1 = [ -b + sqrt( b^2 - 4ac) ] / (2a)
x2 = [ -b - sqrt( b^2 - 4ac) ] / (2a)

I get

x = 24.14 or x = -4.14 approximately.


edit:

jbcoops,

(x+10) * (x-10) = 0

This is x^2 - 100 = 0. The given problem is but x^2 - 20 x - 100 = 0. My answer was right.

To check the correctness of my answer, substitute both values in the original equation and see.

.