Question 57766
Solve for w:
{{{2w(4w+1) = 1}}} First, simplify this by applying the distributive property.
{{{8w^2 + 2w = 1}}} Now subtract 1 from both sides.
{{{8w^2 + 2w - 1 = 0}}} Solve this quadratic equation by factoring.
{{{4w - 1)(2w + 1) = 0}}} Apply the zero product principle.
{{{4w - 1 = 0}}} and/or {{{2w + 1 = 0}}}
If {{{4w - 1 = 0}}} then {{{4w = 1}}} and {{{w = 1/4}}}
If {{{2w + 1 = 0}}} then {{{2w = -1}}} and {{{w = -1/2}}}

The solutions are:
{{{w = 1/4}}}
{{{w = -1/2}}}