Question 587558
{{{ 3x^2-12x-13=0 }}}
Add {{{13}}} to both sides
{{{ 3x^2 - 12x = 13 }}}
Divide both sides by {{{3}}}
{{{ x^2 - 4x = 13/3 }}}
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 - 4x + ((-4)/2)^2 = 13/3 + ((-4)/2)^2 }}}
{{{ x^2 - 4x + (-2)^2 = 13/3 + (-2)^2 }}}
{{{ x^2 - 4x + 4 = 13/3 + 4 }}}
{{{ x^2 - 4x + 4 = 13/3 + 12/3 }}}
{{{ x^2 - 4x + 4 = 25/3 }}}
{{{ ( x - 2 )^2 = ( 5/sqrt(3))^2 }}}
Take the square root of both sides
{{{ x - 2 = 5/sqrt(3) }}}
{{{ x = 2 + 5/sqrt(3) }}}
and also
{{{ x - 2 = -5/sqrt(3) }}}
{{{ x = 2 - 5/sqrt(3) }}}
These are the 2 solutions
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I will check by using approximate values
{{{ x = 2 + 5/1.732 }}}
{{{ x = 2 + 2.8868 }}}
{{{ x = 4.8868 }}}
Plugging this back into original equation
{{{ 3x^2-12x-13=0 }}}
{{{ 3*4.8868^2-12*4.8868-13=0 }}}
{{{ 3*23.8808 - 58.6416 - 13 = 0 }}}
{{{ 71.6424 - 58.6416 - 13 = 0 }}}
{{{ .0008 = 0 }}}
I believe the error is due to rounding off
You can check the other solution