SOLUTION: Find the exact solution to 6x^2+1= -8x by using the Quadratic Formula. A.) -4±√10 B.) (-4±√22)/6 C.) (-2±2√10)/3 D.) (-4±√10)/6

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the exact solution to 6x^2+1= -8x by using the Quadratic Formula. A.) -4±√10 B.) (-4±√22)/6 C.) (-2±2√10)/3 D.) (-4±√10)/6       Log On


   

Question 352265: Find the exact solution to 6x^2+1= -8x by using the Quadratic Formula.
A.) -4±√10
B.) (-4±√22)/6
C.) (-2±2√10)/3
D.) (-4±√10)/6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2%2B1=-8x Start with the given equation.


6x%5E2%2B1%2B8x=0 Add 8x to both sides.


6x%5E2%2B8x%2B1=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=8, 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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%286%29%281%29+%29%29%2F%282%286%29%29 Plug in a=6, b=8, and c=1


x+=+%28-8+%2B-+sqrt%28+64-4%286%29%281%29+%29%29%2F%282%286%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-24+%29%29%2F%282%286%29%29 Multiply 4%286%29%281%29 to get 24


x+=+%28-8+%2B-+sqrt%28+40+%29%29%2F%282%286%29%29 Subtract 24 from 64 to get 40


x+=+%28-8+%2B-+sqrt%28+40+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-8+%2B-+2%2Asqrt%2810%29%29%2F%2812%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-8%2B2%2Asqrt%2810%29%29%2F%2812%29 or x+=+%28-8-2%2Asqrt%2810%29%29%2F%2812%29 Break up the expression.


x+=+%28-4%2Bsqrt%2810%29%29%2F%286%29 or x+=+%28-4-sqrt%2810%29%29%2F%286%29 Reduce.


So the answers are x+=+%28-4%2Bsqrt%2810%29%29%2F%286%29 or x+=+%28-4-sqrt%2810%29%29%2F%286%29


So the answer choice is D)