Solve by extracting square roots.
-$$x ^ { 2 } + 5 x$$
A) $\frac { 25 } { 4 } ; \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$
B) $0 ; ( x + 5 ) ^ { 2 }$
C) $\frac { 25 } { 4 } ; \left( x + \frac { 5 } { 2 } \right) ^ { 2 }$
D) $0 ; \left( x + \frac { 5 } { 2 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

We can factor out an $x$ to get $x(x+5)$, and then we can extract the square root to get $\sqrt{x^2+5x}=\sqrt{x(x+5)}$. Notice that both terms under the square root sign have a factor of $x+5$, so we can simplify further: $\sqrt{x(x+5)}=\sqrt{x}\sqrt{x+5}$. Therefore, the expression can be simplified to $\sqrt{x}\sqrt{x+5}$. We can then square this to get $\left(\sqrt{x}\sqrt{x+5}\right)^2=(x)(x+5)=x^2+5x$. So the answer is $\frac{25}{4}$, which corresponds to choice C.

Solve by Extracting Square Roots x2+5xx ^ { 2 } + 5 xx2+5x

Solve by Extracting Square Roots $x ^ { 2 } + 5 x$