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Simplifying (-8g2 + -3g + 7) + -1(-3g2 + 5g + -5) = 0 Reorder the terms: (7 + -3g + -8g2) + -1(-3g2 + 5g + -5) = 0 Remove parenthesis around (7 + -3g + -8g2) 7 + -3g + -8g2 + -1(-3g2 + 5g + -5) = 0 Reorder the terms: 7 + -3g + -8g2 + -1(-5 + 5g + -3g2) = 0 7 + -3g + -8g2 + (-5 * -1 + 5g * -1 + -3g2 * -1) = 0 7 + -3g + -8g2 + (5 + -5g + 3g2) = 0 Reorder the terms: 7 + 5 + -3g + -5g + -8g2 + 3g2 = 0 Combine like terms: 7 + 5 = 12 12 + -3g + -5g + -8g2 + 3g2 = 0 Combine like terms: -3g + -5g = -8g 12 + -8g + -8g2 + 3g2 = 0 Combine like terms: -8g2 + 3g2 = -5g2 12 + -8g + -5g2 = 0 Solving 12 + -8g + -5g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 1.6g + g2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 1.6g + 2.4 + g2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 1.6g + g2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 1.6g + g2 = 0 + 2.4 1.6g + g2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 1.6g + g2 = 2.4 The g term is 1.6g. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6g + 0.64 + g2 = 2.4 + 0.64 Reorder the terms: 0.64 + 1.6g + g2 = 2.4 + 0.64 Combine like terms: 2.4 + 0.64 = 3.04 0.64 + 1.6g + g2 = 3.04 Factor a perfect square on the left side: (g + 0.8)(g + 0.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (g + 0.8) equal to 1.743559577 and -1.743559577.Subproblem 1
g + 0.8 = 1.743559577 Simplifying g + 0.8 = 1.743559577 Reorder the terms: 0.8 + g = 1.743559577 Solving 0.8 + g = 1.743559577 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + g = 1.743559577 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + g = 1.743559577 + -0.8 g = 1.743559577 + -0.8 Combine like terms: 1.743559577 + -0.8 = 0.943559577 g = 0.943559577 Simplifying g = 0.943559577Subproblem 2
g + 0.8 = -1.743559577 Simplifying g + 0.8 = -1.743559577 Reorder the terms: 0.8 + g = -1.743559577 Solving 0.8 + g = -1.743559577 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + g = -1.743559577 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + g = -1.743559577 + -0.8 g = -1.743559577 + -0.8 Combine like terms: -1.743559577 + -0.8 = -2.543559577 g = -2.543559577 Simplifying g = -2.543559577Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.943559577, -2.543559577}
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