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Simplifying 44x2 + 39x + 6 = 0 Reorder the terms: 6 + 39x + 44x2 = 0 Solving 6 + 39x + 44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. 0.1363636364 + 0.8863636364x + x2 = 0 Move the constant term to the right: Add '-0.1363636364' to each side of the equation. 0.1363636364 + 0.8863636364x + -0.1363636364 + x2 = 0 + -0.1363636364 Reorder the terms: 0.1363636364 + -0.1363636364 + 0.8863636364x + x2 = 0 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + 0.8863636364x + x2 = 0 + -0.1363636364 0.8863636364x + x2 = 0 + -0.1363636364 Combine like terms: 0 + -0.1363636364 = -0.1363636364 0.8863636364x + x2 = -0.1363636364 The x term is 0.8863636364x. Take half its coefficient (0.4431818182). Square it (0.1964101240) and add it to both sides. Add '0.1964101240' to each side of the equation. 0.8863636364x + 0.1964101240 + x2 = -0.1363636364 + 0.1964101240 Reorder the terms: 0.1964101240 + 0.8863636364x + x2 = -0.1363636364 + 0.1964101240 Combine like terms: -0.1363636364 + 0.1964101240 = 0.0600464876 0.1964101240 + 0.8863636364x + x2 = 0.0600464876 Factor a perfect square on the left side: (x + 0.4431818182)(x + 0.4431818182) = 0.0600464876 Calculate the square root of the right side: 0.245043848 Break this problem into two subproblems by setting (x + 0.4431818182) equal to 0.245043848 and -0.245043848.Subproblem 1
x + 0.4431818182 = 0.245043848 Simplifying x + 0.4431818182 = 0.245043848 Reorder the terms: 0.4431818182 + x = 0.245043848 Solving 0.4431818182 + x = 0.245043848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4431818182' to each side of the equation. 0.4431818182 + -0.4431818182 + x = 0.245043848 + -0.4431818182 Combine like terms: 0.4431818182 + -0.4431818182 = 0.0000000000 0.0000000000 + x = 0.245043848 + -0.4431818182 x = 0.245043848 + -0.4431818182 Combine like terms: 0.245043848 + -0.4431818182 = -0.1981379702 x = -0.1981379702 Simplifying x = -0.1981379702Subproblem 2
x + 0.4431818182 = -0.245043848 Simplifying x + 0.4431818182 = -0.245043848 Reorder the terms: 0.4431818182 + x = -0.245043848 Solving 0.4431818182 + x = -0.245043848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4431818182' to each side of the equation. 0.4431818182 + -0.4431818182 + x = -0.245043848 + -0.4431818182 Combine like terms: 0.4431818182 + -0.4431818182 = 0.0000000000 0.0000000000 + x = -0.245043848 + -0.4431818182 x = -0.245043848 + -0.4431818182 Combine like terms: -0.245043848 + -0.4431818182 = -0.6882256662 x = -0.6882256662 Simplifying x = -0.6882256662Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1981379702, -0.6882256662}
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