Question

Given (x – 7)2 = 36, select the values of x.

Answer 1

`\huge\text{Hey there!}`

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

`\mathsf{(x - 7)(x - 7) = 36}`

`\mathsf{x^2 - 14x + 49 = 36}`

`\text{SUBTRACT 36 to BOTH SIDES}`

`\mathsf{x^2 - 14x + 49 + 49 = 36 + 49}`

`\text{Simplify it}`

`\mathsf{x^2 - 14x + 13 = 36 + 49}`

`\mathsf{x^2 - 14x + 13 = 0}`

`\text{FACTOR the LEFT SIDE of your equation}`

`\mathsf{(x - 1)(x - 13) = 0}`

`\text{SET the FACTORS to EQUAL to 0}`

`\mathsf{Equation\ \#1.)\ \rightarrow x - 1 = 0}`

`\mathsf{Equation\ \#2.)\ \rightarrow x - 13 = 0}`

`\text{Simplify it}`

`\mathsf{x = 1 \ or\ x = 13}`

`\huge\text{Thus, your answer should be: } \boxed{\mathsf{x = 1 \ or\ x = 13}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

x=1,13

Explanation:

(x – 7)^2 = 36

To solve for x take the square root of each side

sqrt((x – 7)^2) = sqrt(36)

x-7 = ±6

Splitting into two equations

x-7 = 6 x-7 = -6

Add 7 to all sides

x-7+7 = 6+7 x-7+7 = -6+7

x=13 x=1