Question 194618
.) What number should be added to the expression x2 + 4x to change it into a perfect square trinomial?
:
take 1/2 of the coefficient of the x term and square it
:
{{{x^2+4x+highlight(4)}}} 1/2(4)=2 and 2 squared equals 4 
{{{(x+2)^2}}}

2.) What number should be added to the expression x2 + 12x to change it into a perfect square trinomial? 1/2 of 12 =6 and 6 squared is 36
:
{{{x^2+12x+36}}}
:
{{{(x+6)^2}}}
:

3.)Solve the following equation by transforming it into a perfect square trinomial. 
x2 - 14x = 15 
1/2(14)=7 and 7 squared is 49....so if we add 49 inside the parenthesis then we mus subtract 49 outside the parenthesis to keep equation equivilet
:
{{{x^2-14x+49)-49=15}}}
:
{{{(x-7)^2=64}}}

4.)Solve the following equation by transforming it into a perfect square trinomial. 
3x2 + 18x = 21 
:
{{{3(x^2+6x)=21}}} 1/2(6)=3 and 3 squared is 9
:
{{{3(x^2+6x+9)-27=21}}}.....notice that instead of creating just 9 we have to multiply this by the 3 outside the parathesis 3(9)=27 so we had to subtract 27 to keep equation equivilent
:
{{{3(x+3)^2=48}}}

5) Solve the following equation by transforming it into a perfect square trinomial. 
x2 - 2x = 3
:
take 1/2(2)=1 and 1 squared is 1
:
{{{(x^2-2x+1)-1=3}}}
:
{{{(x-1)^2=4}}}