Answer:
x = 12 and x = -6
Step-by-step explanation:
First subtract 6x on both sides to get a 2nd degree polynomial equal to zero:
[tex]x^2-6x-72=0[/tex]
To complete the square, the formula is to divide 'b' by 2 and square the result. The general form for a 2nd degree polynomial of the variable 'x' is as follows:
[tex]ax^2+bx+c=0[/tex]
For your case, b = 6. Therefore, the term that must be added and subtracted to our equation is:
[tex](6/2)^2=3^2=9[/tex]
Add and subtract 9 to our equation to get:
[tex]x^2-6x+9-9-72=0[/tex]
The first three terms form a perfect square, we have:
[tex](x^2-6x+9)-9-72=0[/tex]
[tex](x^2-6x+9)-81=0[/tex]
What multiplies to equal 9 but adds to equal -6? That would be -3 and -3. Therefore:
[tex](x-3)^2-81=0[/tex]
Add 81 to both sides to get:
[tex](x-3)^2=81[/tex]
We want to take the square root, but recall a square root has a positive and negative branch. Therefore we have two solutions:
[tex]x-3=9[/tex]
[tex]x-3=-9[/tex]
[tex]x=12[/tex]
[tex]x=-6[/tex]
