SOLUTION: Solve the equation. 8x2 + 22x - 6 = 0 x = _____ (smaller value) x = _____ (larger value) I can't solve this, someone help.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve the equation. 8x2 + 22x - 6 = 0 x = _____ (smaller value) x = _____ (larger value) I can't solve this, someone help.      Log On


   

Question 319174: Solve the equation.
8x2 + 22x - 6 = 0
x = _____ (smaller value)
x = _____ (larger value)
I can't solve this, someone help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E2%2B22x-6=0 Start with the given equation.


Notice that the quadratic 8x%5E2%2B22x-6 is in the form of Ax%5E2%2BBx%2BC where A=8, B=22, and C=-6


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-%2822%29+%2B-+sqrt%28+%2822%29%5E2-4%288%29%28-6%29+%29%29%2F%282%288%29%29 Plug in A=8, B=22, and C=-6


x+=+%28-22+%2B-+sqrt%28+484-4%288%29%28-6%29+%29%29%2F%282%288%29%29 Square 22 to get 484.


x+=+%28-22+%2B-+sqrt%28+484--192+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-6%29 to get -192


x+=+%28-22+%2B-+sqrt%28+484%2B192+%29%29%2F%282%288%29%29 Rewrite sqrt%28484--192%29 as sqrt%28484%2B192%29


x+=+%28-22+%2B-+sqrt%28+676+%29%29%2F%282%288%29%29 Add 484 to 192 to get 676


x+=+%28-22+%2B-+sqrt%28+676+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%28-22+%2B-+26%29%2F%2816%29 Take the square root of 676 to get 26.


x+=+%28-22+%2B+26%29%2F%2816%29 or x+=+%28-22+-+26%29%2F%2816%29 Break up the expression.


x+=+%284%29%2F%2816%29 or x+=++%28-48%29%2F%2816%29 Combine like terms.


x+=+1%2F4 or x+=+-3 Simplify.


So the solutions are x+=+1%2F4 or x+=+-3