Question

(p-2)^2=-9 Solve for p​

Answer 1

Answer:

$\displaystyle \boxed{±3i + 4 = p}$

Step-by-step explanation:

(p - 2)² = −9

p² - 4p + 4 = −9

+ 9 + 9

____________

p² - 4p + 13

Since this equation is unfactorable with rational numbers, apply the Quadratic Formula:

$\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = p$

$\displaystyle 4 ± \frac{\sqrt{4^2 - 4[1][13]}}{2[1]} = p$

$\displaystyle 4 ± \frac{\sqrt{16 - 52}}{2} = p$

$\displaystyle 4 ± \frac{\sqrt{-36}}{2} = p$

$\displaystyle 4 ± \frac{6i}{2} = p$

$\displaystyle 4 ± 3i = p$

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

Answer 2

Answer:

Step-by-step explanation: