SOLUTION: 36x^2-12x+1=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 36x^2-12x+1=0      Log On


   

Question 499460: 36x^2-12x+1=0
Found 2 solutions by jim_thompson5910, oberobic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

36x%5E2-12x%2B1=0 Start with the given equation.


Notice that the quadratic 36x%5E2-12x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=36, B=-12, and C=1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2836%29%281%29+%29%29%2F%282%2836%29%29 Plug in A=36, B=-12, and C=1


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2836%29%281%29+%29%29%2F%282%2836%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%2836%29%281%29+%29%29%2F%282%2836%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-144+%29%29%2F%282%2836%29%29 Multiply 4%2836%29%281%29 to get 144


x+=+%2812+%2B-+sqrt%28+0+%29%29%2F%282%2836%29%29 Subtract 144 from 144 to get 0


x+=+%2812+%2B-+sqrt%28+0+%29%29%2F%2872%29 Multiply 2 and 36 to get 72.


x+=+%2812+%2B-+0%29%2F%2872%29 Take the square root of 0 to get 0.


x+=+%2812+%2B+0%29%2F%2872%29 or x+=+%2812+-+0%29%2F%2872%29 Break up the expression.


x+=+%2812%29%2F%2872%29 or x+=++%2812%29%2F%2872%29 Combine like terms.


x+=+1%2F6 or x+=+1%2F6 Simplify.


So the only solution is x+=+1%2F6


Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
factor
36x^2 -12x + 1 = 0
(6x-1)(6x-1) = 0
.
Check with FOIL
36x^2 -6x -6x +1
OK
.
x = 1/6
.
graph%28500%2C500%2C-2%2C2%2C-2%2C2%2C36%2Ax%2Ax-12%2Ax%2B1%29