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Simplifying (1.3g + 3)(4g + 5) = 0 Reorder the terms: (3 + 1.3g)(4g + 5) = 0 Reorder the terms: (3 + 1.3g)(5 + 4g) = 0 Multiply (3 + 1.3g) * (5 + 4g) (3(5 + 4g) + 1.3g * (5 + 4g)) = 0 ((5 * 3 + 4g * 3) + 1.3g * (5 + 4g)) = 0 ((15 + 12g) + 1.3g * (5 + 4g)) = 0 (15 + 12g + (5 * 1.3g + 4g * 1.3g)) = 0 (15 + 12g + (6.5g + 5.2g2)) = 0 Combine like terms: 12g + 6.5g = 18.5g (15 + 18.5g + 5.2g2) = 0 Solving 15 + 18.5g + 5.2g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 5.2 the coefficient of the squared term: Divide each side by '5.2'. 2.884615385 + 3.557692308g + g2 = 0 Move the constant term to the right: Add '-2.884615385' to each side of the equation. 2.884615385 + 3.557692308g + -2.884615385 + g2 = 0 + -2.884615385 Reorder the terms: 2.884615385 + -2.884615385 + 3.557692308g + g2 = 0 + -2.884615385 Combine like terms: 2.884615385 + -2.884615385 = 0.000000000 0.000000000 + 3.557692308g + g2 = 0 + -2.884615385 3.557692308g + g2 = 0 + -2.884615385 Combine like terms: 0 + -2.884615385 = -2.884615385 3.557692308g + g2 = -2.884615385 The g term is 3.557692308g. Take half its coefficient (1.778846154). Square it (3.164293640) and add it to both sides. Add '3.164293640' to each side of the equation. 3.557692308g + 3.164293640 + g2 = -2.884615385 + 3.164293640 Reorder the terms: 3.164293640 + 3.557692308g + g2 = -2.884615385 + 3.164293640 Combine like terms: -2.884615385 + 3.164293640 = 0.279678255 3.164293640 + 3.557692308g + g2 = 0.279678255 Factor a perfect square on the left side: (g + 1.778846154)(g + 1.778846154) = 0.279678255 Calculate the square root of the right side: 0.528846154 Break this problem into two subproblems by setting (g + 1.778846154) equal to 0.528846154 and -0.528846154.Subproblem 1
g + 1.778846154 = 0.528846154 Simplifying g + 1.778846154 = 0.528846154 Reorder the terms: 1.778846154 + g = 0.528846154 Solving 1.778846154 + g = 0.528846154 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.778846154' to each side of the equation. 1.778846154 + -1.778846154 + g = 0.528846154 + -1.778846154 Combine like terms: 1.778846154 + -1.778846154 = 0.000000000 0.000000000 + g = 0.528846154 + -1.778846154 g = 0.528846154 + -1.778846154 Combine like terms: 0.528846154 + -1.778846154 = -1.25 g = -1.25 Simplifying g = -1.25Subproblem 2
g + 1.778846154 = -0.528846154 Simplifying g + 1.778846154 = -0.528846154 Reorder the terms: 1.778846154 + g = -0.528846154 Solving 1.778846154 + g = -0.528846154 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.778846154' to each side of the equation. 1.778846154 + -1.778846154 + g = -0.528846154 + -1.778846154 Combine like terms: 1.778846154 + -1.778846154 = 0.000000000 0.000000000 + g = -0.528846154 + -1.778846154 g = -0.528846154 + -1.778846154 Combine like terms: -0.528846154 + -1.778846154 = -2.307692308 g = -2.307692308 Simplifying g = -2.307692308Solution
The solution to the problem is based on the solutions from the subproblems. g = {-1.25, -2.307692308}
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