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Simplifying z2 + -2.667z + 1.778 = 0 Reorder the terms: 1.778 + -2.667z + z2 = 0 Solving 1.778 + -2.667z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-1.778' to each side of the equation. 1.778 + -2.667z + -1.778 + z2 = 0 + -1.778 Reorder the terms: 1.778 + -1.778 + -2.667z + z2 = 0 + -1.778 Combine like terms: 1.778 + -1.778 = 0.000 0.000 + -2.667z + z2 = 0 + -1.778 -2.667z + z2 = 0 + -1.778 Combine like terms: 0 + -1.778 = -1.778 -2.667z + z2 = -1.778 The z term is -2.667z. Take half its coefficient (-1.3335). Square it (1.77822225) and add it to both sides. Add '1.77822225' to each side of the equation. -2.667z + 1.77822225 + z2 = -1.778 + 1.77822225 Reorder the terms: 1.77822225 + -2.667z + z2 = -1.778 + 1.77822225 Combine like terms: -1.778 + 1.77822225 = 0.00022225 1.77822225 + -2.667z + z2 = 0.00022225 Factor a perfect square on the left side: (z + -1.3335)(z + -1.3335) = 0.00022225 Calculate the square root of the right side: 0.014908052 Break this problem into two subproblems by setting (z + -1.3335) equal to 0.014908052 and -0.014908052.Subproblem 1
z + -1.3335 = 0.014908052 Simplifying z + -1.3335 = 0.014908052 Reorder the terms: -1.3335 + z = 0.014908052 Solving -1.3335 + z = 0.014908052 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.3335' to each side of the equation. -1.3335 + 1.3335 + z = 0.014908052 + 1.3335 Combine like terms: -1.3335 + 1.3335 = 0.0000 0.0000 + z = 0.014908052 + 1.3335 z = 0.014908052 + 1.3335 Combine like terms: 0.014908052 + 1.3335 = 1.348408052 z = 1.348408052 Simplifying z = 1.348408052Subproblem 2
z + -1.3335 = -0.014908052 Simplifying z + -1.3335 = -0.014908052 Reorder the terms: -1.3335 + z = -0.014908052 Solving -1.3335 + z = -0.014908052 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.3335' to each side of the equation. -1.3335 + 1.3335 + z = -0.014908052 + 1.3335 Combine like terms: -1.3335 + 1.3335 = 0.0000 0.0000 + z = -0.014908052 + 1.3335 z = -0.014908052 + 1.3335 Combine like terms: -0.014908052 + 1.3335 = 1.318591948 z = 1.318591948 Simplifying z = 1.318591948Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.348408052, 1.318591948}
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