Question

(p-2)^2=-9 Solve for p​

Answer 1

`\displaystyle \boxed{±3i + 4 = p}`

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 ± (√(b^2 - 4ac))/(2a) = p`

`\displaystyle 4 ± (√(4^2 - 4[1][13]))/(2[1]) = p`

`\displaystyle 4 ± (√(16 - 52))/(2) = p`

`\displaystyle 4 ± (√(-36))/(2) = p`

`\displaystyle 4 ± (6i)/(2) = p`

`\displaystyle 4 ± 3i = p`

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

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