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40 votes
40 votes
Solve for xxx. Enter the solutions from least to greatest. Round to two decimal places. (x - 6)^2 - 5 = 0

User TheClassic
by
2.2k points

1 Answer

22 votes
22 votes

Add 5 to both sides of the equation.


\boldsymbol{\sf{(x-6)^(2)-5=0 }}

Take the square root of both sides to eliminate the exponent on the left side.


\boldsymbol{\sf{x-6=\pm√(5) }}

The complete solution is the result of the positive or negative portions of the solution.

First, use the positive value of ± to find the first solution.


\boldsymbol{\sf{x-6=√(5) }}

Add 6 to both sides of the equation.


\boldsymbol{ \sf{x=√(5)+6 }}

Then use the negative value of ± to find the second solution.


\boldsymbol{\sf{x-6=-√(5) }}

Add 6 to both sides of the equation.


\boldsymbol{\sf{x=-√(5)+6 }}

The complete solution is the result of the positive or negative portions of the solution.


\boldsymbol{\sf{x=√(5)+6,-√(5)+6 }}


\huge \red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ x=\pm√(5)+6 }}}}

Skandar

User David Shortman
by
3.2k points