SOLUTION: 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 p

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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 p      Log On


   

Question 136350This question is from textbook Algebra 1
: Could you please help me? I am so lost on how to do these.... x%5E2%2B7x=-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. This question is from textbook Algebra 1

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please help me? I am so lost on how to do these.... x%5E2%2B7x=-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%5E2%2B7x=-12
Multiply 7 by 1%2F2, getting 7%2F2.
Now square 7%2F2. %287%2F2%29%5E2=49%2F4
Now add 49%2F4 to both sides:
x%5E2%2B7x%2B49%2F4=-12%2B+49%2F4
write the -12 as %28-12%29%2F1
x%5E2%2B7x%2B49%2F4=%28-12%29%2F1%2B+49%2F4
The LCD on the right is 4, so multiply %28-12%29%2F1 by 4%2F4
x%5E2%2B7x%2B49%2F4=+++%28+%28-12%29%2F1+%29%2A%284%2F4%29%2B+49%2F4++
x%5E2%2B7x%2B49%2F4=%28%28-48%29%2F4%29%2B+49%2F4
x%5E2%2B7x%2B49%2F4=1%2F4
Now factor the left side:
%28x%2B7%2F2%29%28x%2B7%2F2%29=1%2F4
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:
%28x%2B7%2F2%29%5E2=1%2F4
Next we use the principle of square roots:
x%2B7%2F2= ±sqrt%281%2F4%29
x%2B7%2F2= ±1%2F2
Now we solve for x by adding -7%2F2 to both sides:
x%2B7%2F2-7%2F2= ±1%2F2-7%2F2
x= ±1%2F2-7%2F2
Using the +
x= +1%2F2-7%2F2
x= -6%2F2
x+=+-3
Using the -
x= -1%2F2-7%2F2
x=+-8%2F2
x+=+-4
Edwin