Question 136350
Could you please help me? I am so lost on how to do these....   {{{x^2+7x=-12}}}   I tried to do the part where you take half of b and got 3.5... then squared it to get 12.25 and put it back in for c and got  x^2+7x+12.25=-12+12.25 but i"m lost other than that.  We're supposed to be "solving quadratic equations by completing the square" if it helps any.

 {{{x^2+7x=-12}}}

Multiply {{{7}}} by {{{1/2}}}, getting {{{7/2}}}.
Now square {{{7/2}}}.  {{{(7/2)^2=49/4}}}
Now add {{{49/4}}} to both sides:

   {{{x^2+7x+49/4=-12+ 49/4}}}

write the {{{-12}}} as {{{(-12)/1}}}

   {{{x^2+7x+49/4=(-12)/1+ 49/4}}}

The LCD on the right is {{{4}}}, so multiply {{{(-12)/1}}} by {{{4/4}}}

   {{{x^2+7x+49/4=   ( (-12)/1 )*(4/4)+ 49/4  }}}   

   {{{x^2+7x+49/4=((-48)/4)+ 49/4}}}

   {{{x^2+7x+49/4=1/4}}}

Now factor the left side:

   {{{(x+7/2)(x+7/2)=1/4}}}

The left side is a perfect square (that's why the method is
called "completing the square").  So we write the left side
as a square, the square of a binomial:

   {{{(x+7/2)^2=1/4}}}

Next we use the principle of square roots:

   {{{x+7/2}}}= ±{{{sqrt(1/4)}}}

    {{{x+7/2}}}= ±{{{1/2}}}

Now we solve for x by adding {{{-7/2}}} to both sides:

    {{{x+7/2-7/2}}}= ±{{{1/2-7/2}}}

            {{{x}}}= ±{{{1/2-7/2}}}

Using the +

            {{{x}}}= +{{{1/2-7/2}}}

            {{{x}}}= {{{-6/2}}}

             {{{x = -3}}}

Using the -

            {{{x}}}= {{{-1/2-7/2}}}

            {{{x= -8/2}}}

             {{{x = -4}}}

Edwin