j^2+4j=45

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Solution for j^2+4j=45 equation:


Simplifying
j2 + 4j = 45

Reorder the terms:
4j + j2 = 45

Solving
4j + j2 = 45

Solving for variable 'j'.

Reorder the terms:
-45 + 4j + j2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 4j + j2 = 0

Factor a trinomial.
(-9 + -1j)(5 + -1j) = 0

Subproblem 1

Set the factor '(-9 + -1j)' equal to zero and attempt to solve: Simplifying -9 + -1j = 0 Solving -9 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1j = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1j = 0 + 9 -1j = 0 + 9 Combine like terms: 0 + 9 = 9 -1j = 9 Divide each side by '-1'. j = -9 Simplifying j = -9

Subproblem 2

Set the factor '(5 + -1j)' equal to zero and attempt to solve: Simplifying 5 + -1j = 0 Solving 5 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1j = 0 + -5 -1j = 0 + -5 Combine like terms: 0 + -5 = -5 -1j = -5 Divide each side by '-1'. j = 5 Simplifying j = 5

Solution

j = {-9, 5}

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