Question

Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answer 1

`\boxed{\tt{x=13}}`

`\boxed{\tt{x=1}}`

Explanation:

`\textsf{We are asked to identify correct values for x.}`

`\textsf{We are given an equation and 4 values of x.}`

`\textsf{Let's start by Substituting.}`

`\textsf{Replace the value of x with a given value, or known value.}`

`\tt(x-7)^(2)=36`

`\Large\underline{\textsf{Substitute 13 into x:}}`

`\tt(13-7)^(2)=36`

`\tt6^(2)=36`

`\tt36=36 \ \checkmark`

`\Large\underline{\textsf{Substitute 1 into x:}}`

`\tt(1-7)^(2)=36`

`\tt-6^(2)=36`

`\textsf{Remember that -6 is being multiplied by itself. Hence, the product is positive.}`

`\tt36=36 \ \checkmark`

`\Large\underline{\textsf{Substitute -29 into x:}}`

`\tt(-29-7)^(2)=36`

`\tt(-36)^(2)=36`

`1296 \\eq 36`

`\Large\underline{\textsf{Substitute 42 into x:}}`

`\tt(42-7)^(2)=36`

`\tt35^(2)=36`

`\tt1225 \\eq 36`

`\large\underline{\textsf{The correct solutions are;}}`

`\boxed{\tt{x=13}}`

`\boxed{\tt{x=1}}`