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Simplifying 14j2 + 42j + 63 = 0 Reorder the terms: 63 + 42j + 14j2 = 0 Solving 63 + 42j + 14j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '7'. 7(9 + 6j + 2j2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(9 + 6j + 2j2)' equal to zero and attempt to solve: Simplifying 9 + 6j + 2j2 = 0 Solving 9 + 6j + 2j2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 3j + j2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 3j + -4.5 + j2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 3j + j2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 3j + j2 = 0 + -4.5 3j + j2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 3j + j2 = -4.5 The j term is 3j. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3j + 2.25 + j2 = -4.5 + 2.25 Reorder the terms: 2.25 + 3j + j2 = -4.5 + 2.25 Combine like terms: -4.5 + 2.25 = -2.25 2.25 + 3j + j2 = -2.25 Factor a perfect square on the left side: (j + 1.5)(j + 1.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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