8g^2-g-3=0

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Solution for 8g^2-g-3=0 equation:


Simplifying
8g2 + -1g + -3 = 0

Reorder the terms:
-3 + -1g + 8g2 = 0

Solving
-3 + -1g + 8g2 = 0

Solving for variable 'g'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.375 + -0.125g + g2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.125g + 0.375 + g2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.125g + g2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.125g + g2 = 0 + 0.375
-0.125g + g2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.125g + g2 = 0.375

The g term is -0.125g.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125g + 0.00390625 + g2 = 0.375 + 0.00390625

Reorder the terms:
0.00390625 + -0.125g + g2 = 0.375 + 0.00390625

Combine like terms: 0.375 + 0.00390625 = 0.37890625
0.00390625 + -0.125g + g2 = 0.37890625

Factor a perfect square on the left side:
(g + -0.0625)(g + -0.0625) = 0.37890625

Calculate the square root of the right side: 0.615553613

Break this problem into two subproblems by setting 
(g + -0.0625) equal to 0.615553613 and -0.615553613.

Subproblem 1

g + -0.0625 = 0.615553613 Simplifying g + -0.0625 = 0.615553613 Reorder the terms: -0.0625 + g = 0.615553613 Solving -0.0625 + g = 0.615553613 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + g = 0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + g = 0.615553613 + 0.0625 g = 0.615553613 + 0.0625 Combine like terms: 0.615553613 + 0.0625 = 0.678053613 g = 0.678053613 Simplifying g = 0.678053613

Subproblem 2

g + -0.0625 = -0.615553613 Simplifying g + -0.0625 = -0.615553613 Reorder the terms: -0.0625 + g = -0.615553613 Solving -0.0625 + g = -0.615553613 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + g = -0.615553613 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + g = -0.615553613 + 0.0625 g = -0.615553613 + 0.0625 Combine like terms: -0.615553613 + 0.0625 = -0.553053613 g = -0.553053613 Simplifying g = -0.553053613

Solution

The solution to the problem is based on the solutions from the subproblems. g = {0.678053613, -0.553053613}

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