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Simplifying -3g + -2 + -1(4g + 10) * g = 6 Reorder the terms: -3g + -2 + -1(10 + 4g) * g = 6 Reorder the terms for easier multiplication: -3g + -2 + -1g(10 + 4g) = 6 -3g + -2 + (10 * -1g + 4g * -1g) = 6 -3g + -2 + (-10g + -4g2) = 6 Reorder the terms: -2 + -3g + -10g + -4g2 = 6 Combine like terms: -3g + -10g = -13g -2 + -13g + -4g2 = 6 Solving -2 + -13g + -4g2 = 6 Solving for variable 'g'. Reorder the terms: -2 + -6 + -13g + -4g2 = 6 + -6 Combine like terms: -2 + -6 = -8 -8 + -13g + -4g2 = 6 + -6 Combine like terms: 6 + -6 = 0 -8 + -13g + -4g2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 13g + 4g2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 13g + 4g2)' equal to zero and attempt to solve: Simplifying 8 + 13g + 4g2 = 0 Solving 8 + 13g + 4g2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 3.25g + g2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.25g + -2 + g2 = 0 + -2 Reorder the terms: 2 + -2 + 3.25g + g2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.25g + g2 = 0 + -2 3.25g + g2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.25g + g2 = -2 The g term is 3.25g. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25g + 2.640625 + g2 = -2 + 2.640625 Reorder the terms: 2.640625 + 3.25g + g2 = -2 + 2.640625 Combine like terms: -2 + 2.640625 = 0.640625 2.640625 + 3.25g + g2 = 0.640625 Factor a perfect square on the left side: (g + 1.625)(g + 1.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (g + 1.625) equal to 0.80039053 and -0.80039053.Subproblem 1
g + 1.625 = 0.80039053 Simplifying g + 1.625 = 0.80039053 Reorder the terms: 1.625 + g = 0.80039053 Solving 1.625 + g = 0.80039053 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + g = 0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + g = 0.80039053 + -1.625 g = 0.80039053 + -1.625 Combine like terms: 0.80039053 + -1.625 = -0.82460947 g = -0.82460947 Simplifying g = -0.82460947Subproblem 2
g + 1.625 = -0.80039053 Simplifying g + 1.625 = -0.80039053 Reorder the terms: 1.625 + g = -0.80039053 Solving 1.625 + g = -0.80039053 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + g = -0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + g = -0.80039053 + -1.625 g = -0.80039053 + -1.625 Combine like terms: -0.80039053 + -1.625 = -2.42539053 g = -2.42539053 Simplifying g = -2.42539053Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.82460947, -2.42539053}Solution
g = {-0.82460947, -2.42539053}
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