SOLUTION: I actually have five questions. 1.) What number should be added to the expression x2 + 4x to change it into a perfect square trinomial? 2.) What number should be added

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I actually have five questions. 1.) What number should be added to the expression x2 + 4x to change it into a perfect square trinomial? 2.) What number should be added      Log On


   



Question 194618: I actually have five questions.

1.) What number should be added to the expression x2 + 4x to change it into a perfect square trinomial?


2.) What number should be added to the expression x2 + 12x to change it into a perfect square trinomial?





3.)Solve the following equation by transforming it into a perfect square trinomial.
x2 - 14x = 15




4.)Solve the following equation by transforming it into a perfect square trinomial.
3x2 + 18x = 21




5.) Solve the following equation by transforming it into a perfect square trinomial.
x2 - 2x = 3

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
.) 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%5E2%2B4x%2Bhighlight%284%29 1/2(4)=2 and 2 squared equals 4
%28x%2B2%29%5E2
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%5E2%2B12x%2B36
:
%28x%2B6%29%5E2
:
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%5E2-14x%2B49%29-49=15
:
%28x-7%29%5E2=64
4.)Solve the following equation by transforming it into a perfect square trinomial.
3x2 + 18x = 21
:
3%28x%5E2%2B6x%29=21 1/2(6)=3 and 3 squared is 9
:
3%28x%5E2%2B6x%2B9%29-27=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%28x%2B3%29%5E2=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
:
%28x%5E2-2x%2B1%29-1=3
:
%28x-1%29%5E2=4