Question

Need help to do this step by step please
3x2 - 2x=-1

Answer 1

Solving the expression
`3x^2-2x=-1` we get:
`\mathbf{x=(1+√(2)i )/(3)\:or\:x=(1-√(2)i )/(3)}`

Explanation:

We need to solve the expression:
`3x^2-2x=-1`

This is a quadratic expression and it can be solved using quadratic formula

Solving:

`3x^2-2x=-1\\`

we can write it as:

`3x^2-2x+1=0`

The quadratic formula is:
`x=(-b\pm√(b^2-4ac))/(2a)`

where a = 3, b = -2 and c= 1

Putting values and solving:

`x=(-b\pm√(b^2-4ac))/(2a)\\x=(-(-2)\pm√((-2)^2-4(3)(1)))/(2(3))\\x=(2\pm√(4-12))/(2(3))\\x=(2\pm√(-8))/(6)\\We\:know\:that\:√(-1)=i\\x=(2\pm√(8)√(-1) )/(6) \\We\:know\:√(8)=√(2* 2 * 2)=√(2^2 * 2)=2√(2) \\x=(2\pm2√(2)i )/(6)\\Now,\\x=(2+2√(2)i )/(6)\:or\:x=(2-2√(2)i )/(6)\\x=(2(1+√(2)i) )/(6)\:or\:x=(2(1-√(2)i) )/(6)\\x=(1+√(2)i )/(3)\:or\:x=(1-√(2)i )/(3)`

So, solving the expression
`3x^2-2x=-1` we get:
`\mathbf{x=(1+√(2)i )/(3)\:or\:x=(1-√(2)i )/(3)}`