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Simplifying 2j + j(j + -3) = 17 Reorder the terms: 2j + j(-3 + j) = 17 2j + (-3 * j + j * j) = 17 2j + (-3j + j2) = 17 Combine like terms: 2j + -3j = -1j -1j + j2 = 17 Solving -1j + j2 = 17 Solving for variable 'j'. Reorder the terms: -17 + -1j + j2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -1j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -1j + 17 + j2 = 0 + 17 Reorder the terms: -17 + 17 + -1j + j2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1j + j2 = 0 + 17 -1j + j2 = 0 + 17 Combine like terms: 0 + 17 = 17 -1j + j2 = 17 The j term is -1j. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1j + 0.25 + j2 = 17 + 0.25 Reorder the terms: 0.25 + -1j + j2 = 17 + 0.25 Combine like terms: 17 + 0.25 = 17.25 0.25 + -1j + j2 = 17.25 Factor a perfect square on the left side: (j + -0.5)(j + -0.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (j + -0.5) equal to 4.153311931 and -4.153311931.Subproblem 1
j + -0.5 = 4.153311931 Simplifying j + -0.5 = 4.153311931 Reorder the terms: -0.5 + j = 4.153311931 Solving -0.5 + j = 4.153311931 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + j = 4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + j = 4.153311931 + 0.5 j = 4.153311931 + 0.5 Combine like terms: 4.153311931 + 0.5 = 4.653311931 j = 4.653311931 Simplifying j = 4.653311931Subproblem 2
j + -0.5 = -4.153311931 Simplifying j + -0.5 = -4.153311931 Reorder the terms: -0.5 + j = -4.153311931 Solving -0.5 + j = -4.153311931 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + j = -4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + j = -4.153311931 + 0.5 j = -4.153311931 + 0.5 Combine like terms: -4.153311931 + 0.5 = -3.653311931 j = -3.653311931 Simplifying j = -3.653311931Solution
The solution to the problem is based on the solutions from the subproblems. j = {4.653311931, -3.653311931}
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