Question

What is the solution of the equation (4x + 3)^2 = 18 or (4x +3) squared =18?

Answer 1

We have to solve this expression:

`(4x+3)^2=18`

This can be expressed as a quadratic equation, so we will probably get two solutions.

We can start by writing:

`\begin{gathered} (4x+3)^2=18 \\ 4x+3=\pm√(18) \\ 4x=-3\pm√(18) \\ x=(-3\pm√(18))/(4) \end{gathered}`

We can simplify it a little further as:

`\begin{gathered} x=(-3\pm√(18))/(4) \\ x=(-3\pm√(9*2))/(4) \\ x=(-3\pm3√(2))/(4) \\ x=(3)/(4)(1\pm√(2)) \\ =>x_1=(3)/(4)(1-√(2)) \\ =>x_2=(3)/(4)(1+√(2)) \end{gathered}`

Answer: the solutions are 3/4*(1-√2) and 3/4*(1+√2).