Question

solve for v.
$2v^2 - 6v - 20 = (v - 2)^2$
if there is more than one solution, separate them with commas.
$v = $

Explanation:

Step1: Expand right-hand side

$(x-2)^2 = x^2 -4x +4$

Step2: Rearrange all terms to left side

$2x^2 -6x -20 -x^2 +4x -4 = 0$

Step3: Simplify the quadratic equation

$x^2 -2x -24 = 0$

Step4: Factor the quadratic

$(x-6)(x+4) = 0$

Step5: Solve for x

Set each factor equal to 0:
$x-6=0 \implies x=6$
$x+4=0 \implies x=-4$

Answer:

$6, -4$