Question

How do I solve equations bt extracting square roots?

Ex.

`3(x + {4)}^(2) = 8`
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Answer 1

`x=(2√(6))/(3)-4,\:x=-(2√(6))/(3)-4`

Explanation:

`3(x+4)^2 =8\\\\\mathrm{Divide\:both\:sides\:by\:}3\\(3\left(x+4\right)^2)/(3)=(8)/(3)\\\\Simplify\\\left(x+4\right)^2=(8)/(3)\\\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}\\g\left(x\right)=√(f\left(a\right)),\:\:-√(f\left(a\right))\\\mathrm{Solve\:}\:x+4=\sqrt{(8)/(3)}:\\\quad x=(2√(6))/(3)-4\\\\\\\mathrm{Solve\:}\:x+4=-\sqrt{(8)/(3)}:\\\quad x=-(2√(6))/(3)-4\\`

`x=(2√(6))/(3)-4,\:x=-(2√(6))/(3)-4`