Remove the radical by raising each side to the index of the radical.
x=-1
Answer:
x = -6 and x= -1
Step-by-step explanation:
the expression we have is:
[tex]x+4=\sqrt{x+10}[/tex]
Taking tha square of the whole equation:
[tex](x+4)^2=x+10[/tex]
solving the binomial squared on the left side with the rule:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
we get:
[tex]x^2+8x+16=x+10[/tex]
rearranging all terms to the left:
[tex]x^2+8x-x+16-10=0[/tex]
joining like terms:
[tex]x^2+7x+6=0[/tex]
we can sove this quadratic equation with the quadratic formula, or by factoring:
[tex]x^2+7x+6=(x+6)(x+1)=0[/tex]
and from this we find our two solutions using the zero product property (if a product of thing is equal to zero, one of them must be zero)
[tex]x+6=0\\x=-6[/tex]
and
[tex]x+1=0\\x=-1[/tex]
