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Simplifying 7j2 + -6j + -8 = 0 Reorder the terms: -8 + -6j + 7j2 = 0 Solving -8 + -6j + 7j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -0.8571428571j + j2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.8571428571j + 1.142857143 + j2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.8571428571j + j2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.8571428571j + j2 = 0 + 1.142857143 -0.8571428571j + j2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.8571428571j + j2 = 1.142857143 The j term is -0.8571428571j. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571j + 0.1836734694 + j2 = 1.142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571j + j2 = 1.142857143 + 0.1836734694 Combine like terms: 1.142857143 + 0.1836734694 = 1.3265306124 0.1836734694 + -0.8571428571j + j2 = 1.3265306124 Factor a perfect square on the left side: (j + -0.4285714286)(j + -0.4285714286) = 1.3265306124 Calculate the square root of the right side: 1.151751107 Break this problem into two subproblems by setting (j + -0.4285714286) equal to 1.151751107 and -1.151751107.Subproblem 1
j + -0.4285714286 = 1.151751107 Simplifying j + -0.4285714286 = 1.151751107 Reorder the terms: -0.4285714286 + j = 1.151751107 Solving -0.4285714286 + j = 1.151751107 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + j = 1.151751107 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + j = 1.151751107 + 0.4285714286 j = 1.151751107 + 0.4285714286 Combine like terms: 1.151751107 + 0.4285714286 = 1.5803225356 j = 1.5803225356 Simplifying j = 1.5803225356Subproblem 2
j + -0.4285714286 = -1.151751107 Simplifying j + -0.4285714286 = -1.151751107 Reorder the terms: -0.4285714286 + j = -1.151751107 Solving -0.4285714286 + j = -1.151751107 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + j = -1.151751107 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + j = -1.151751107 + 0.4285714286 j = -1.151751107 + 0.4285714286 Combine like terms: -1.151751107 + 0.4285714286 = -0.7231796784 j = -0.7231796784 Simplifying j = -0.7231796784Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.5803225356, -0.7231796784}
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