Answer:
Explanation:
Step1: isolate the square root on the left hand side.
Original equation :x+1=√-6x-6
Isolate :x+1=√-6x-6.
Step2: raise both sides to the second power.
(x+1)^2=(√-6x-6)^2
(x+1)(x+1)=-6x-6
Step3: after squaring, solve the quadratic equation.
x^2+2x-1=-6x-6
x^2+8x+7=0
x^2+7x+x+7=0
x(x+7)+1(x+7)=0
(x+1)(x+7)=0
x=-1,-7
Step4:check that the first solution correct.
Input x=-1 into the original equation
x+1=√-6x-6
-1+1=√+6-6
0=0
Step5:check that the second equation is correct.
Input x=-7 into the original equation
x+1=√-6x-6
-7+1=√42-6
-6=√36
-6#6
Therefore one solution is found.
x=-1