z^2-760z+5776=0

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Solution for z^2-760z+5776=0 equation:


Simplifying
z2 + -760z + 5776 = 0

Reorder the terms:
5776 + -760z + z2 = 0

Solving
5776 + -760z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-5776' to each side of the equation.
5776 + -760z + -5776 + z2 = 0 + -5776

Reorder the terms:
5776 + -5776 + -760z + z2 = 0 + -5776

Combine like terms: 5776 + -5776 = 0
0 + -760z + z2 = 0 + -5776
-760z + z2 = 0 + -5776

Combine like terms: 0 + -5776 = -5776
-760z + z2 = -5776

The z term is -760z.  Take half its coefficient (-380).
Square it (144400) and add it to both sides.

Add '144400' to each side of the equation.
-760z + 144400 + z2 = -5776 + 144400

Reorder the terms:
144400 + -760z + z2 = -5776 + 144400

Combine like terms: -5776 + 144400 = 138624
144400 + -760z + z2 = 138624

Factor a perfect square on the left side:
(z + -380)(z + -380) = 138624

Calculate the square root of the right side: 372.322440903

Break this problem into two subproblems by setting 
(z + -380) equal to 372.322440903 and -372.322440903.

Subproblem 1

z + -380 = 372.322440903 Simplifying z + -380 = 372.322440903 Reorder the terms: -380 + z = 372.322440903 Solving -380 + z = 372.322440903 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '380' to each side of the equation. -380 + 380 + z = 372.322440903 + 380 Combine like terms: -380 + 380 = 0 0 + z = 372.322440903 + 380 z = 372.322440903 + 380 Combine like terms: 372.322440903 + 380 = 752.322440903 z = 752.322440903 Simplifying z = 752.322440903

Subproblem 2

z + -380 = -372.322440903 Simplifying z + -380 = -372.322440903 Reorder the terms: -380 + z = -372.322440903 Solving -380 + z = -372.322440903 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '380' to each side of the equation. -380 + 380 + z = -372.322440903 + 380 Combine like terms: -380 + 380 = 0 0 + z = -372.322440903 + 380 z = -372.322440903 + 380 Combine like terms: -372.322440903 + 380 = 7.677559097 z = 7.677559097 Simplifying z = 7.677559097

Solution

The solution to the problem is based on the solutions from the subproblems. z = {752.322440903, 7.677559097}

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