Question

Solve the equation by completing the square.4x(x + 6) = -40

Answer 1

The solution to the equation is;

`\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}`

Step-by-step explanation:

Given the equation below;

`4x(x+6)=-40`

Expanding the bracket we have;

`4x^2+24x=-40`

dividing through by 4;

`\begin{gathered} (4x^2)/(4)+(24)/(4)x=-(40)/(4) \\ x^2+6x=-10 \end{gathered}`

To solve by completing the square, let us add the square of half of 6 to both sides;

`\begin{gathered} x^2+6x+((6)/(2))^2=-10+((6)/(2))^2 \\ x^2+6x+9=-10+9 \\ x^2+6x+9=-1 \\ (x+3)^2=-1 \end{gathered}`

taking square roots of both sides;

`\begin{gathered} x+3=\sqrt[]{-1} \\ x+3=\pm i \end{gathered}`

So;

`\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}`

Therefore, the solution to the equation is;

`\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}`