z^2-2.667z+1.778=0

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Solution for z^2-2.667z+1.778=0 equation:


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 = 1.348408052

Subproblem 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 = 1.318591948

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.348408052, 1.318591948}

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