z^2-1.72z+0.72=0

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Solution for z^2-1.72z+0.72=0 equation:


Simplifying
z2 + -1.72z + 0.72 = 0

Reorder the terms:
0.72 + -1.72z + z2 = 0

Solving
0.72 + -1.72z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-0.72' to each side of the equation.
0.72 + -1.72z + -0.72 + z2 = 0 + -0.72

Reorder the terms:
0.72 + -0.72 + -1.72z + z2 = 0 + -0.72

Combine like terms: 0.72 + -0.72 = 0.00
0.00 + -1.72z + z2 = 0 + -0.72
-1.72z + z2 = 0 + -0.72

Combine like terms: 0 + -0.72 = -0.72
-1.72z + z2 = -0.72

The z term is -1.72z.  Take half its coefficient (-0.86).
Square it (0.7396) and add it to both sides.

Add '0.7396' to each side of the equation.
-1.72z + 0.7396 + z2 = -0.72 + 0.7396

Reorder the terms:
0.7396 + -1.72z + z2 = -0.72 + 0.7396

Combine like terms: -0.72 + 0.7396 = 0.0196
0.7396 + -1.72z + z2 = 0.0196

Factor a perfect square on the left side:
(z + -0.86)(z + -0.86) = 0.0196

Calculate the square root of the right side: 0.14

Break this problem into two subproblems by setting 
(z + -0.86) equal to 0.14 and -0.14.

Subproblem 1

z + -0.86 = 0.14 Simplifying z + -0.86 = 0.14 Reorder the terms: -0.86 + z = 0.14 Solving -0.86 + z = 0.14 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.86' to each side of the equation. -0.86 + 0.86 + z = 0.14 + 0.86 Combine like terms: -0.86 + 0.86 = 0.00 0.00 + z = 0.14 + 0.86 z = 0.14 + 0.86 Combine like terms: 0.14 + 0.86 = 1 z = 1 Simplifying z = 1

Subproblem 2

z + -0.86 = -0.14 Simplifying z + -0.86 = -0.14 Reorder the terms: -0.86 + z = -0.14 Solving -0.86 + z = -0.14 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.86' to each side of the equation. -0.86 + 0.86 + z = -0.14 + 0.86 Combine like terms: -0.86 + 0.86 = 0.00 0.00 + z = -0.14 + 0.86 z = -0.14 + 0.86 Combine like terms: -0.14 + 0.86 = 0.72 z = 0.72 Simplifying z = 0.72

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1, 0.72}

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