Question

(x+5)^2/3=4

Answer 1

Multiply both sides of the equation by 3.

(x+5)^2=4⋅(3)

Multiply 4 by each term inside the parentheses.

(x+5^)2=12

Take the square root of each side of the equation to setup the solution for x.

(x+5)^2⋅1/2=±12−−√

Remove the perfect root factor (x+5) under the radical to solve for x.

(x+5)=±12−−√

Multiply 2 by 3√ to get 23√.

(x+5)=±23√

First, substitute in the + portion of the ± to find the first solution.

(x+5)=23√

Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.

x=−5+23√

Move all terms not containing x to the right-hand side of the equation.

x=23√−5

Next, substitute in the − portion of the ± to find the second solution.

(x+5)=−23√

Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.

x=−5−23√

Move all terms not containing x to the right-hand side of the equation.

x=−23√−5

The complete solution is the result of both the + and − portions of the solution.

x=23√−5,−23√−5
x≈−1.535898384862,−8.464101615138