What number is added to each side of the equation $4 x ^ { 2 } + 48 x = 7$ in completing the square?
A) 75
B) 36
C) 4
D) 48

Question

Quizplus · Accepted Answer

To complete the square, take half of the coefficient of $x$ (which is 48), square it, and add it to both sides. Half of 48 is 24, and 24 squared is 576. However, since the equation is $4x^2 + 48x$, you first factor out the 4: $4(x^2 + 12x)$. Then, take half of 12, which is 6, square it to get 36, and add 36 inside the parentheses. Since the 4 was factored out, you actually add $4 \times 36 = 144$ to both sides, but the number added inside the parentheses is 36.

What Number Is Added to Each Side of the Equation 4x2+48x=74 x ^ { 2 } + 48 x = 74x2+48x=7

What Number Is Added to Each Side of the Equation $4 x ^ { 2 } + 48 x = 7$