Solve by extracting square roots.
-$x ^ { 2 } - 10 x$
A) $25 ; ( x - 5 ) ^ { 2 }$
B) $0 ; ( x - 5 ) ^ { 2 }$
C) $25 ; ( x + 5 ) ^ { 2 }$
D) $25 ; ( x - 10 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The given expression is $x^2 - 10x$. To solve by extracting square roots, we need to complete the square. First, take half of the coefficient of $x$, which is $-10/2 = -5$, and square it to get $25$. Adding and subtracting $25$ inside the expression gives $x^2 - 10x + 25 - 25$. This simplifies to $(x - 5)^2 - 25$, but since we're only completing the square, the correct representation is $(x - 5)^2$, and the $25$ is the number we added to complete the square, making choice A correct.

Solve by Extracting Square Roots x2−10xx ^ { 2 } - 10 xx2−10x

Solve by Extracting Square Roots $x ^ { 2 } - 10 x$