Question

Solve the quadratic equation by root method. Show all steps.

Answer 1

The root method requires us to leave the expression that is raised to the power of 2 on one side of the equality. We do so, by applying mathematical operations on both sides of the equation

We begin with the equation

`2(x-4)^(2)-6=18`

First, we add 6 on both sides, so we get

`2(x-4)^(2)=18+6=24`

Then, we divide boths sides by 2, so we get

`(x-4)^(2)=(24)/(2)=12`

Now, we take the square root on both sides. Have in mind that once we take the square root we should consider the positive and negative root. So we get

`x-4=\pm\sqrt[]{12}`

Finally, we add 4 on both sides, so we get

`x=4\pm\sqrt[]{12}`

This is equivalent to have the solutions

`x=4+\sqrt[]{12}`

and

`x=4-\sqrt[]{12}`