Solve the following quadratic equation for all values of x in simplest form. 3(x - 7) ^(2) + 34 = 46

Question

Solve the following quadratic equation for all values of x in simplest form.
`3(x - 7) ^(2) + 34 = 46`

Answer 1

Given

`3(x-7)^2+34=46`

Procedure

`\begin{gathered} 3(x^2-14x+49)+34=46 \\ 3x^2-42x+149+34-46=0 \\ 3x^2-42x+135 \end{gathered}`

Solving

`\begin{gathered} x^2-14x+45 \\ (x-5)(x-9) \end{gathered}`

x = 5

x = 9