Question

solve for v.
2v² - 5v + 18 = (v + 2)²
if there is more than one solution, separate them with commas.
v =

Explanation:

Step1: Expand right-hand side

$(v+2)^2 = v^2 + 4v + 4$

Step2: Rearrange equation to standard form

Subtract $v^2 + 4v + 4$ from both sides:
$2v^2 -5v +18 - v^2 -4v -4 = 0$
Simplify: $v^2 -9v +14 = 0$

Step3: Factor the quadratic

Find two numbers that multiply to 14 and add to -9: -2 and -7.
$(v-2)(v-7) = 0$

Step4: Solve for $v$

Set each factor equal to 0:
$v-2=0$ or $v-7=0$

Answer:

$v = 2, 7$