Question

пfStudy the steps shown to solve the given equation.V30 - 2x = x-330-2x = x2 - 6x + 90 = x2 - 4x - 210 = (x + 3)(x-7)Based on the above work, possible solutions of the equationDONE

Answer 1

Given:

`\sqrt[]{30-2x}=x-3`

Taking square root on both sides, we get

`30-2x=(x-3)^2`

`30-2x=x^2-6x+9`

Adding 2x-30 to both sides, we get

`30-2x+2x-30=x^2-6x+9+2x-30`

`0=x^2-4x-21`

`0=x^2-3x+7x-21`

`0=x(x-3)+7(x-3)`

`0=(x-3)(x+7)`

`(x-3)(x+7)=0`

`(x-3)=0,(x+7)=0`

`x-3+3=0+3,x+7-7=0-7`
`x=3,x=-7`

Hence the solutions are

`-7,3`