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

$-7,3$