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1 solution
Hello, like what the title said, do not be fooled into thinking that you can factorise the left hand side of the equation to a^2+2ab+b^2.
7x+7+2(49x^2+7x-42)^(1/2) + 7x-6 = 182 - (7x+7)^(1/2) - (7x-6)^(1/2)
Then ((7x+7)^(1/2) + (7x-6)^(1/2))^2 = 182 - (7x+7)^(1/2) - (7x-6)^(1/2)
Let a = (7x+7)^(1/2) + (7x-6)^(1/2) so that a^2 = 182 - a. Solving we get a=-14 or 13 but we reject the negative solution as square roots are always positive.
Solving for x we get x=6.