1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.
2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.
Here, that looks like ...
4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4
4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation
4(x +5)² = 180 . . . . . . . . . . . written as a square
The given expression is
The greatest common factor is .
We factor to obtain;
The given quadratic equation is
We split the middle term to obtain
Factor by grouping;
Use zero product property;
The given system of equation is
If we multiply by 3, we obtain;
If we multiply by 4 we obtain;
Adding the last two equations will give us;
The y-variable is eliminated.
by 3. Multiply 7x−3y=6 by 4. Add the resulting equations together.