```Question 352265

{{{6x^2+1+8x=0}}} Add 8x to both sides.

{{{6x^2+8x+1=0}}} Combine like terms.

Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=6}}}, {{{b=8}}}, and {{{c=1}}}

Let's use the quadratic formula to solve for x

{{{x = (-(8) +- sqrt( (8)^2-4(6)(1) ))/(2(6))}}} Plug in  {{{a=6}}}, {{{b=8}}}, and {{{c=1}}}

{{{x = (-8 +- sqrt( 64-4(6)(1) ))/(2(6))}}} Square {{{8}}} to get {{{64}}}.

{{{x = (-8 +- sqrt( 64-24 ))/(2(6))}}} Multiply {{{4(6)(1)}}} to get {{{24}}}

{{{x = (-8 +- sqrt( 40 ))/(2(6))}}} Subtract {{{24}}} from {{{64}}} to get {{{40}}}

{{{x = (-8 +- sqrt( 40 ))/(12)}}} Multiply {{{2}}} and {{{6}}} to get {{{12}}}.

{{{x = (-8 +- 2*sqrt(10))/(12)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)

{{{x = (-8+2*sqrt(10))/(12)}}} or {{{x = (-8-2*sqrt(10))/(12)}}} Break up the expression.

{{{x = (-4+sqrt(10))/(6)}}} or {{{x = (-4-sqrt(10))/(6)}}} Reduce.

So the answers are {{{x = (-4+sqrt(10))/(6)}}} or {{{x = (-4-sqrt(10))/(6)}}}

So the answer choice is D)```