Question

Solve the equation 3x2 + 6x - 1 = 8.

Answer 1

Given:

The equation is:

`\begin{gathered} 3x^2+6x-1=8 \\ 3x^2+6x-1-8=0 \\ 3x^2+6x-9=0 \end{gathered}`

Take out common 3 from the equation.

`\begin{gathered} 3(x^2+2x-3)=0 \\ x^2+2x-3=0 \end{gathered}`

This is a quadratic equation.

The standard form of the quadratic equation is:

`ax^2+bx+c=0`

Then the solution of this equation is given as:

`x=(-b\pm√(b^2-4ac))/(2a)`

The solution of the equation is:

`\begin{gathered} x=(-2\pm√((2)^2-4(1)(-3)))/(2(1)) \\ x=(-2\pm√(4+12))/(2) \\ x=(-2\pm√(16))/(2) \\ x=(-2\pm4)/(2) \end{gathered}`

Take + sign

`\begin{gathered} x=(-2+4)/(2) \\ x=(2)/(2) \\ x=1 \end{gathered}`

Take - sign

`\begin{gathered} x=(-2-4)/(2) \\ x=(-6)/(2) \\ x=-3 \end{gathered}`

Final Answer:

The solution of the given equation is x= -3, 1.