g^2-g=323

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Solution for g^2-g=323 equation:


Simplifying
g2 + -1g = 323

Reorder the terms:
-1g + g2 = 323

Solving
-1g + g2 = 323

Solving for variable 'g'.

Reorder the terms:
-323 + -1g + g2 = 323 + -323

Combine like terms: 323 + -323 = 0
-323 + -1g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '323' to each side of the equation.
-323 + -1g + 323 + g2 = 0 + 323

Reorder the terms:
-323 + 323 + -1g + g2 = 0 + 323

Combine like terms: -323 + 323 = 0
0 + -1g + g2 = 0 + 323
-1g + g2 = 0 + 323

Combine like terms: 0 + 323 = 323
-1g + g2 = 323

The g term is -1g.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1g + 0.25 + g2 = 323 + 0.25

Reorder the terms:
0.25 + -1g + g2 = 323 + 0.25

Combine like terms: 323 + 0.25 = 323.25
0.25 + -1g + g2 = 323.25

Factor a perfect square on the left side:
(g + -0.5)(g + -0.5) = 323.25

Calculate the square root of the right side: 17.979154596

Break this problem into two subproblems by setting 
(g + -0.5) equal to 17.979154596 and -17.979154596.

Subproblem 1

g + -0.5 = 17.979154596 Simplifying g + -0.5 = 17.979154596 Reorder the terms: -0.5 + g = 17.979154596 Solving -0.5 + g = 17.979154596 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + g = 17.979154596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = 17.979154596 + 0.5 g = 17.979154596 + 0.5 Combine like terms: 17.979154596 + 0.5 = 18.479154596 g = 18.479154596 Simplifying g = 18.479154596

Subproblem 2

g + -0.5 = -17.979154596 Simplifying g + -0.5 = -17.979154596 Reorder the terms: -0.5 + g = -17.979154596 Solving -0.5 + g = -17.979154596 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + g = -17.979154596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + g = -17.979154596 + 0.5 g = -17.979154596 + 0.5 Combine like terms: -17.979154596 + 0.5 = -17.479154596 g = -17.479154596 Simplifying g = -17.479154596

Solution

The solution to the problem is based on the solutions from the subproblems. g = {18.479154596, -17.479154596}

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