Question

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

Answer 1

`\large\fbox{\textsf{x = 13, 1.}}`

Explanation:

`\textsf{For this problem, we are asked to substitute possible values of x.}`

`\Large\underline{\textsf{What is Substitution?}}`

`\textsf{\underline{Substitution} is \underline{replacing} an \underline{unknown value} with a \underline{known value}.}`

`\textsf{Unknown values can be represented as variables, as for this problem.}`

`\large\underline{\textsf{We are given 4 options:}}`

`\mathtt{x = 13}`

`\mathtt{x = 1}`

`\mathtt{x = -29}`

`\mathtt{x = 42}`

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

`\large\underline{\textsf{Equation:}}`

`\mathtt{(x-7)^(2)=36}`

`\large\underline{\textsf{Substitute 13:}}`

`\mathtt{(13-7)^(2)=36}`

`\mathtt{6^(2)=36}`

`\mathtt{36=36} \ \checkmark`

`\large\underline{\textsf{Substitute 1:}}`

`\mathtt{(1-7)^(2)=36}`

`\mathtt{-6^(2)=36}`

`\mathtt{36=36} \ \checkmark`

`\large\underline{\textsf{Substitute -29:}}`

`\mathtt{(-29-7)^(2)=36}`

`\mathtt{-36^(2)=36}`

`\mathtt{ 1296 \\eq 36}`

`\large\underline{\textsf{Substitute 42:}}`

`\mathtt{(42-7)^(2)=36}`

`\mathtt{35^(2)=36}`

`\mathtt{1235 \\eq 36}`