Question 118925
Remember;

{{{(a+b)^2=a^2+2ab+b^2}}}


GIVEN:

{{{x^2+8x+13}}}


Here, {{{a^2=x^2}}} so {{{a=x}}}

Also, here, {{{2ab=8x}}} so {{{ab=4x}}}

We have {{{ab=4x}}} and {{{a=x}}}

Solving simultaneously,

{{{(x)b=4x}}}
{{{bx=4x}}}
{{{b=4}}}


Now we know {{{a=x}}} and {{{b=4}}}


Finding {{{(a+b)^2}}},

{{{(a+b)^2=(x+4)^2=x^2+2(4x)+16=x^2+8x+16}}}


To be {{{x^2+8x+16}}}, we just add 3 to {{{x^2+8x+13}}},


{{{x^2+8x+13=0}}}
{{{x^2+8x+13+3=0+3}}}
{{{x^2+8x+16=3}}}
{{{(x+4)^2=3}}}
{{{sqrt((x+4)^2)=sqrt(3)}}}
{{{x+4=0+-sqrt(3)}}}
{{{x=4+-sqrt(3)}}}


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HyperBrain!