5(8+3g)g=2

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Solution for 5(8+3g)g=2 equation:


Simplifying
5(8 + 3g) * g = 2

Reorder the terms for easier multiplication:
5g(8 + 3g) = 2
(8 * 5g + 3g * 5g) = 2
(40g + 15g2) = 2

Solving
40g + 15g2 = 2

Solving for variable 'g'.

Reorder the terms:
-2 + 40g + 15g2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 40g + 15g2 = 0

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

Divide each side by '15'.
-0.1333333333 + 2.666666667g + g2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + 2.666666667g + 0.1333333333 + g2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + 2.666666667g + g2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + 2.666666667g + g2 = 0 + 0.1333333333
2.666666667g + g2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
2.666666667g + g2 = 0.1333333333

The g term is 2.666666667g.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667g + 1.777777780 + g2 = 0.1333333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667g + g2 = 0.1333333333 + 1.777777780

Combine like terms: 0.1333333333 + 1.777777780 = 1.9111111133
1.777777780 + 2.666666667g + g2 = 1.9111111133

Factor a perfect square on the left side:
(g + 1.333333334)(g + 1.333333334) = 1.9111111133

Calculate the square root of the right side: 1.382429424

Break this problem into two subproblems by setting 
(g + 1.333333334) equal to 1.382429424 and -1.382429424.

Subproblem 1

g + 1.333333334 = 1.382429424 Simplifying g + 1.333333334 = 1.382429424 Reorder the terms: 1.333333334 + g = 1.382429424 Solving 1.333333334 + g = 1.382429424 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + g = 1.382429424 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + g = 1.382429424 + -1.333333334 g = 1.382429424 + -1.333333334 Combine like terms: 1.382429424 + -1.333333334 = 0.04909609 g = 0.04909609 Simplifying g = 0.04909609

Subproblem 2

g + 1.333333334 = -1.382429424 Simplifying g + 1.333333334 = -1.382429424 Reorder the terms: 1.333333334 + g = -1.382429424 Solving 1.333333334 + g = -1.382429424 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + g = -1.382429424 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + g = -1.382429424 + -1.333333334 g = -1.382429424 + -1.333333334 Combine like terms: -1.382429424 + -1.333333334 = -2.715762758 g = -2.715762758 Simplifying g = -2.715762758

Solution

The solution to the problem is based on the solutions from the subproblems. g = {0.04909609, -2.715762758}

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