-3j^2-54j+15=0

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Solution for -3j^2-54j+15=0 equation:


Simplifying
-3j2 + -54j + 15 = 0

Reorder the terms:
15 + -54j + -3j2 = 0

Solving
15 + -54j + -3j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -18j + -1j2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -18j + -1j2)' equal to zero and attempt to solve: Simplifying 5 + -18j + -1j2 = 0 Solving 5 + -18j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 18j + j2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 18j + 5 + j2 = 0 + 5 Reorder the terms: -5 + 5 + 18j + j2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 18j + j2 = 0 + 5 18j + j2 = 0 + 5 Combine like terms: 0 + 5 = 5 18j + j2 = 5 The j term is 18j. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18j + 81 + j2 = 5 + 81 Reorder the terms: 81 + 18j + j2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + 18j + j2 = 86 Factor a perfect square on the left side: (j + 9)(j + 9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (j + 9) equal to 9.273618495 and -9.273618495.

Subproblem 1

j + 9 = 9.273618495 Simplifying j + 9 = 9.273618495 Reorder the terms: 9 + j = 9.273618495 Solving 9 + j = 9.273618495 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + j = 9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + j = 9.273618495 + -9 j = 9.273618495 + -9 Combine like terms: 9.273618495 + -9 = 0.273618495 j = 0.273618495 Simplifying j = 0.273618495

Subproblem 2

j + 9 = -9.273618495 Simplifying j + 9 = -9.273618495 Reorder the terms: 9 + j = -9.273618495 Solving 9 + j = -9.273618495 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + j = -9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + j = -9.273618495 + -9 j = -9.273618495 + -9 Combine like terms: -9.273618495 + -9 = -18.273618495 j = -18.273618495 Simplifying j = -18.273618495

Solution

The solution to the problem is based on the solutions from the subproblems. j = {0.273618495, -18.273618495}

Solution

j = {0.273618495, -18.273618495}

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