Solve Quadratic Equations by Completing the Square
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + 18 x$$
A) $81 ; x ^ { 2 } + 18 x + 81 = ( x + 9 ) ^ { 2 }$
B) $9 ; x ^ { 2 } + 18 x + 9 = ( x + 81 ) ^ { 2 }$
C) $324 ; x ^ { 2 } + 18 x + 324 = ( x + 18 ) ^ { 2 }$
D) $18 ; x ^ { 2 } + 18 x + 18 = ( x + 324 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

To complete the square, we need to add $\left(\frac{18}{2}\right)^2=81$ to the binomial. This gives us $x^2+18x+81=(x+9)^2$, which is a perfect square trinomial. Therefore, the constant we need to add is 81 and the correct choice is A.

Solve Quadratic Equations by Completing the Square Determine the Constant x2+18xx ^ { 2 } + 18 xx2+18x

Solve Quadratic Equations by Completing the Square
Determine the Constant $x ^ { 2 } + 18 x$