3g^2-9g-14=0

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Solution for 3g^2-9g-14=0 equation:


Simplifying
3g2 + -9g + -14 = 0

Reorder the terms:
-14 + -9g + 3g2 = 0

Solving
-14 + -9g + 3g2 = 0

Solving for variable 'g'.

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

Divide each side by '3'.
-4.666666667 + -3g + g2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -3g + 4.666666667 + g2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -3g + g2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -3g + g2 = 0 + 4.666666667
-3g + g2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-3g + g2 = 4.666666667

The g term is -3g.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3g + 2.25 + g2 = 4.666666667 + 2.25

Reorder the terms:
2.25 + -3g + g2 = 4.666666667 + 2.25

Combine like terms: 4.666666667 + 2.25 = 6.916666667
2.25 + -3g + g2 = 6.916666667

Factor a perfect square on the left side:
(g + -1.5)(g + -1.5) = 6.916666667

Calculate the square root of the right side: 2.62995564

Break this problem into two subproblems by setting 
(g + -1.5) equal to 2.62995564 and -2.62995564.

Subproblem 1

g + -1.5 = 2.62995564 Simplifying g + -1.5 = 2.62995564 Reorder the terms: -1.5 + g = 2.62995564 Solving -1.5 + g = 2.62995564 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + g = 2.62995564 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + g = 2.62995564 + 1.5 g = 2.62995564 + 1.5 Combine like terms: 2.62995564 + 1.5 = 4.12995564 g = 4.12995564 Simplifying g = 4.12995564

Subproblem 2

g + -1.5 = -2.62995564 Simplifying g + -1.5 = -2.62995564 Reorder the terms: -1.5 + g = -2.62995564 Solving -1.5 + g = -2.62995564 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + g = -2.62995564 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + g = -2.62995564 + 1.5 g = -2.62995564 + 1.5 Combine like terms: -2.62995564 + 1.5 = -1.12995564 g = -1.12995564 Simplifying g = -1.12995564

Solution

The solution to the problem is based on the solutions from the subproblems. g = {4.12995564, -1.12995564}

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