z^2-2.9*z+1=0

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Solution for z^2-2.9*z+1=0 equation:


Simplifying
z2 + -2.9z + 1 = 0

Reorder the terms:
1 + -2.9z + z2 = 0

Solving
1 + -2.9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.9z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + -2.9z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.9z + z2 = 0 + -1
-2.9z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.9z + z2 = -1

The z term is -2.9z.  Take half its coefficient (-1.45).
Square it (2.1025) and add it to both sides.

Add '2.1025' to each side of the equation.
-2.9z + 2.1025 + z2 = -1 + 2.1025

Reorder the terms:
2.1025 + -2.9z + z2 = -1 + 2.1025

Combine like terms: -1 + 2.1025 = 1.1025
2.1025 + -2.9z + z2 = 1.1025

Factor a perfect square on the left side:
(z + -1.45)(z + -1.45) = 1.1025

Calculate the square root of the right side: 1.05

Break this problem into two subproblems by setting 
(z + -1.45) equal to 1.05 and -1.05.

Subproblem 1

z + -1.45 = 1.05 Simplifying z + -1.45 = 1.05 Reorder the terms: -1.45 + z = 1.05 Solving -1.45 + z = 1.05 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + z = 1.05 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + z = 1.05 + 1.45 z = 1.05 + 1.45 Combine like terms: 1.05 + 1.45 = 2.5 z = 2.5 Simplifying z = 2.5

Subproblem 2

z + -1.45 = -1.05 Simplifying z + -1.45 = -1.05 Reorder the terms: -1.45 + z = -1.05 Solving -1.45 + z = -1.05 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + z = -1.05 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + z = -1.05 + 1.45 z = -1.05 + 1.45 Combine like terms: -1.05 + 1.45 = 0.4 z = 0.4 Simplifying z = 0.4

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.5, 0.4}

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