Question 157876
a) Move the constant term to the right side of the equation.
1){{{ x^2 - 2x - 13 = 0}}}
 {{{x^2 - 2x = 13}}} 

b) Multiply each term in the equation by four times the coefficient of the {{{x^2}}} term.
the coefficient of the {{{x^2}}} is {{{1}}} and four times the coefficient will be {{{4*1=4}}}, so you will have:
{{{x^2*4 - 2x*4 = 13*4}}}
{{{4x^2 - 8x = 52}}}

c) Square the coefficient of the original {{{x }}}term and add it to both sides of the equation.
the coefficient of the original {{{x }}}term is {{{-2}}}
{{{4x^2 - 8x + (-2)^2  = 52 + (-2)^2}}}

{{{4x^2 - 8x + 4 = 52 + 4}}}…then you have
{{{4x^2 - 8x + 4 = 56}}}
{{{(2x-2)^2= 56}}}

d) Take the square root of both sides.

{{{sqrt((2x-2)^2)}}} = +-{{{sqrt(56)}}}
{{{2x-2}}} = +-{{{(7.48)}}}


e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for {{{x}}}.

{{{2x-2 = 7.48}}}
{{{2x = 7.48+2}}}
{{{2x = 9.48}}}
{{{x = 9.48/2}}}
{{{x = 4.74}}}


f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for {{{x}}}. 

{{{2x-2 = -7.48}}}
{{{2x = -7.48+2}}}
{{{2x = -5.48}}}
{{{x = -5.48/2}}}
{{{x = -2.74}}}



2) {{{2x^2 - 3x - 5 = 0}}}

a)	Move the constant term to the right side of the equation.
{{{2x^2 - 3x = 5 }}}

b) Multiply each term in the equation by four times the coefficient of the {{{x^2}}} term.
the coefficient of the {{{x^2}}} is {{{2}}} and four times the coefficient will be {{{4*2= 8}}}, so you will have:

{{{2x^2*8 - 3x*8 = 5*8 }}}

{{{16x^2 -24*x = 40 }}}


c) Square the coefficient of the original {{{x }}}term and add it to both sides of the equation.
the coefficient of the original {{{x }}}term is {{{-3}}}
{{{16x^2 - 24x + (-3)^2 = 40 +  (-3)^2 }}}
{{{16x^2 - 24x + 9 = 40 +  9 }}}
{{{16x^2 - 24x + 9 = 49 }}}

{{{(4x-3)^2= 49}}}


d) Take the square root of both sides

{{{sqrt((4x-3)^2)= sqrt(49)}}}

{{{4x-3}}} = +-{{{(7)}}}


e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for {{{x}}}.

{{{4x-3}}} = +{{{(7)}}}
{{{4x = 7+3 }}}
{{{4x = 10 }}}

{{{x = 10/4}}}
{{{x = 2.5}}}


f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for {{{x}}}.

{{{4x-3}}} = -{{{(7)}}}
{{{4x = -7+3 }}}
{{{4x = -4 }}}

{{{x = -4/4}}}
{{{x = -1}}}