which equation has the same solution as $x^{2}+18x + 19=-7$?\na $(x - 9)^{2}=-107$\nb $(x + 9)^{2}=-107$\nc…

which equation has the same solution as $x^{2}+18x + 19=-7$?\na $(x - 9)^{2}=-107$\nb $(x + 9)^{2}=-107$\nc $(x - 9)^{2}=55$\nd $(x + 9)^{2}=55$

which equation has the same solution as $x^{2}+18x + 19=-7$?\na $(x - 9)^{2}=-107$\nb $(x + 9)^{2}=-107$\nc $(x - 9)^{2}=55$\nd $(x + 9)^{2}=55$

Answer

Explanation:

Step1: Rewrite the given equation

First, rewrite $x^{2}+18x + 19=-7$ as $x^{2}+18x+26 = 0$.

Step2: Complete the square

For the quadratic expression $x^{2}+18x$, according to the formula $(a + b)^2=a^{2}+2ab + b^{2}$, here $a = x$, $2ab=18x$, so $b = 9$. $x^{2}+18x=(x + 9)^{2}-81$. The original equation $x^{2}+18x+26 = 0$ can be rewritten as $(x + 9)^{2}-81+26=0$.

Step3: Simplify the equation

Simplify $(x + 9)^{2}-81+26=0$ to get $(x + 9)^{2}-55=0$, that is $(x + 9)^{2}=55$.

Answer:

D. $(x + 9)^{2}=55$