Question 315345
{{{3x^2+8x-2=0}}}
1. Solve using Quadratic formula
<pre><b>
{{{a=3}}}, {{{b=8}}}, {{{c=-2}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-8 +- sqrt( 8^2-4*3*(-2) ))/(2*3) }}}
{{{x = (-8 +- sqrt( 64+24 ))/6 }}}
{{{x = (-8 +- sqrt(88 ))/6 }}}
{{{x = (-8 +- sqrt(4*22 ))/6 }}}
{{{x = (-8 +- 2*sqrt(22 ))/6 }}}
{{{x = (2(-4 +- sqrt(22 )))/6 }}}
{{{x = (-4 +- sqrt(22 ))/3 }}}
</pre></b>
2. Solve using completing the square
<pre><b>
{{{3x^2+8x-2=0}}}

Get the constant term on the right and only x-terms on the left

{{{3x^2+8x=2}}}

Divide through by 3

{{{x^2+(8/3)x=2/3}}}

Multiply the coefficient of x by {{{1/2}}}:  {{{(8/3)(1/2)=8/6=4/3}}}
Square that value:  {{{(4/3)^2=16/9}}}
Add that value to both sides:

{{{x^2+(8/3)x+16/9=2/3+16/9}}}

Factor the left side: {{{(x+4/3)(x+4/3)}}} or {{{(x+4/3)^2}}}
Combine fractions on the right side: {{{2/3+16/9=(2*3)/(3*3)+16/9=6/9+16/9=22/9}}}

{{{(x+4/3)^2=22/9}}}

Take square roots of both sides:

{{{x+4/3=""+-sqrt(22/9)}}}

{{{x+4/3=""+-sqrt(22)/3}}}

Add {{{-4/3}}} to both sides:

{{{x=-4/3+-sqrt(22)/3}}}

{{{x=(-4+-sqrt(22))/3}}}

</pre></b>
3. Tell which method you prefer and why
<pre><b>
The quadratic formula because it's usually easier.

Edwin</pre>