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Simplifying z2 + -2.66666667z + 1.777777777778 = 0 Reorder the terms: 1.777777777778 + -2.66666667z + z2 = 0 Solving 1.777777777778 + -2.66666667z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-1.777777777778' to each side of the equation. 1.777777777778 + -2.66666667z + -1.777777777778 + z2 = 0 + -1.777777777778 Reorder the terms: 1.777777777778 + -1.777777777778 + -2.66666667z + z2 = 0 + -1.777777777778 Combine like terms: 1.777777777778 + -1.777777777778 = 0.000000000000 0.000000000000 + -2.66666667z + z2 = 0 + -1.777777777778 -2.66666667z + z2 = 0 + -1.777777777778 Combine like terms: 0 + -1.777777777778 = -1.777777777778 -2.66666667z + z2 = -1.777777777778 The z term is -2.66666667z. Take half its coefficient (-1.333333335). Square it (1.777777782) and add it to both sides. Add '1.777777782' to each side of the equation. -2.66666667z + 1.777777782 + z2 = -1.777777777778 + 1.777777782 Reorder the terms: 1.777777782 + -2.66666667z + z2 = -1.777777777778 + 1.777777782 Combine like terms: -1.777777777778 + 1.777777782 = 0.000000004222 1.777777782 + -2.66666667z + z2 = 0.000000004222 Factor a perfect square on the left side: (z + -1.333333335)(z + -1.333333335) = 0.000000004222 Calculate the square root of the right side: 0.000064977 Break this problem into two subproblems by setting (z + -1.333333335) equal to 0.000064977 and -0.000064977.Subproblem 1
z + -1.333333335 = 0.000064977 Simplifying z + -1.333333335 = 0.000064977 Reorder the terms: -1.333333335 + z = 0.000064977 Solving -1.333333335 + z = 0.000064977 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.333333335' to each side of the equation. -1.333333335 + 1.333333335 + z = 0.000064977 + 1.333333335 Combine like terms: -1.333333335 + 1.333333335 = 0.000000000 0.000000000 + z = 0.000064977 + 1.333333335 z = 0.000064977 + 1.333333335 Combine like terms: 0.000064977 + 1.333333335 = 1.333398312 z = 1.333398312 Simplifying z = 1.333398312Subproblem 2
z + -1.333333335 = -0.000064977 Simplifying z + -1.333333335 = -0.000064977 Reorder the terms: -1.333333335 + z = -0.000064977 Solving -1.333333335 + z = -0.000064977 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.333333335' to each side of the equation. -1.333333335 + 1.333333335 + z = -0.000064977 + 1.333333335 Combine like terms: -1.333333335 + 1.333333335 = 0.000000000 0.000000000 + z = -0.000064977 + 1.333333335 z = -0.000064977 + 1.333333335 Combine like terms: -0.000064977 + 1.333333335 = 1.333268358 z = 1.333268358 Simplifying z = 1.333268358Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.333398312, 1.333268358}
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