How do you solve 7+sqrt(8-x)=127+8x=12 algebraically and graphically?

2 Answers
Jul 3, 2018

The solution is x=-17x=17

Explanation:

The equation is

7+sqrt(8-x)=127+8x=12

=>, sqrt(8-x)=12-7=58x=127=5

Squaring both sides

(sqrt(8-x))^2=5^2(8x)2=52

=>, 8-x=258x=25

=>, x=8-25=-17

Graphically, plot the curve

sqrt(8-x)+7-12=08x+712=0

sqrt(8-x)-5=08x5=0

graph{sqrt(8-x)-5 [-30.25, 10.3, -8.68, 11.58]}

And the solution to the equation is the point where the curve intercepts with the x-axis, that is (-17,0)(17,0)

Jul 3, 2018

I tried this:

Explanation:

1) Algebraically:
rearrange:

sqrt(8-x)=12-78x=127

sqrt(8-x)=58x=5

square both:

(sqrt(8-x))^2=5^2(8x)2=52

8-x=258x=25

x=-25+8=-17x=25+8=17

2) Graphically:
graph{(y-7-sqrt(8-x))(y-12)=0 [-50.02, 14.96, -3.34, 29.11]}