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Simplifying 3g2 + -6g + -14 = 3g Reorder the terms: -14 + -6g + 3g2 = 3g Solving -14 + -6g + 3g2 = 3g Solving for variable 'g'. Reorder the terms: -14 + -6g + -3g + 3g2 = 3g + -3g Combine like terms: -6g + -3g = -9g -14 + -9g + 3g2 = 3g + -3g Combine like terms: 3g + -3g = 0 -14 + -9g + 3g2 = 0 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 = 4.12995564Subproblem 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 = -1.12995564Solution
The solution to the problem is based on the solutions from the subproblems. g = {4.12995564, -1.12995564}
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