Answer:
Option B
Option C
Step-by-step explanation:
[tex]x^{2} +2x=4[/tex]
we need to divide the coefficient of x by half since it is required for completing square, this term is added and subtracted at the same time to keep the equation intact, so we have
[tex]x^{2} +2x+1-1=4[/tex]
later we have
[tex](x+1)^{2} -1=4[/tex]
[tex](x+1)^{2}= 4+1[/tex]
[tex](x+1)^{2} = 5[/tex]
[tex]\sqrt{(x+1)^{2}} =\sqrt{5}[/tex]
we know
[tex]\sqrt[2]{a^{2}} = abs (a)[/tex]
[tex]abs(x+1)=\sqrt{5}[/tex]
we have
[tex]x+1=\sqrt{5}[/tex]
or
[tex]x+1= -\sqrt{5}[/tex]
so we have
[tex]x=\sqrt{5}-1[/tex]
[tex]x=-\sqrt{5}-1[/tex]
finally
[tex]x=+- \sqrt{5}-1[/tex]
The second is obtained by summing the two given equations
f(x)=8x-10
g(x)=3x+5
-----------------
f(x)+g(x)=11x-5
