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Simplifying j(j + 3) = 28 Reorder the terms: j(3 + j) = 28 (3 * j + j * j) = 28 (3j + j2) = 28 Solving 3j + j2 = 28 Solving for variable 'j'. Reorder the terms: -28 + 3j + j2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 3j + j2 = 0 Factor a trinomial. (-7 + -1j)(4 + -1j) = 0Subproblem 1
Set the factor '(-7 + -1j)' equal to zero and attempt to solve: Simplifying -7 + -1j = 0 Solving -7 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1j = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1j = 0 + 7 -1j = 0 + 7 Combine like terms: 0 + 7 = 7 -1j = 7 Divide each side by '-1'. j = -7 Simplifying j = -7Subproblem 2
Set the factor '(4 + -1j)' equal to zero and attempt to solve: Simplifying 4 + -1j = 0 Solving 4 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1j = 0 + -4 -1j = 0 + -4 Combine like terms: 0 + -4 = -4 -1j = -4 Divide each side by '-1'. j = 4 Simplifying j = 4Solution
j = {-7, 4}
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