Question 438421
{{{ 10x^2 = 20x + 30 }}}
Subtract {{{20x}}} from both sides
{{{ 10x^2 - 20x = 30 }}}
Divide both sides by {{{10}}}
{{{ x^2 - 2x = 3 }}}
Now you can complete the square.
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 - 2x + (-2/2)^2 = (-2/2)^2 + 3 }}}
{{{ x^2 - 2x + 1 = 1 + 3 }}}
Both sides are now a perfect square
{{{ ( x - 1 )^2 = 2^2 }}}
Take the square root of both sides
{{{ x - 1 = 2 }}} ( this is the (+) square root)
{{{ x = 3 }}}
and
{{{ x - 1 = -2 }}} (this is the (-) square root)
{{{ x = -1 }}}
The solutions are {{{x=3}}} and {{{x=-1}}}