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Simplifying 9.3x(x) + 5.7x + -2.3 = 0 Multiply x * x 9.3x2 + 5.7x + -2.3 = 0 Reorder the terms: -2.3 + 5.7x + 9.3x2 = 0 Solving -2.3 + 5.7x + 9.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.3 the coefficient of the squared term: Divide each side by '9.3'. -0.247311828 + 0.6129032258x + x2 = 0 Move the constant term to the right: Add '0.247311828' to each side of the equation. -0.247311828 + 0.6129032258x + 0.247311828 + x2 = 0 + 0.247311828 Reorder the terms: -0.247311828 + 0.247311828 + 0.6129032258x + x2 = 0 + 0.247311828 Combine like terms: -0.247311828 + 0.247311828 = 0.000000000 0.000000000 + 0.6129032258x + x2 = 0 + 0.247311828 0.6129032258x + x2 = 0 + 0.247311828 Combine like terms: 0 + 0.247311828 = 0.247311828 0.6129032258x + x2 = 0.247311828 The x term is 0.6129032258x. Take half its coefficient (0.3064516129). Square it (0.09391259105) and add it to both sides. Add '0.09391259105' to each side of the equation. 0.6129032258x + 0.09391259105 + x2 = 0.247311828 + 0.09391259105 Reorder the terms: 0.09391259105 + 0.6129032258x + x2 = 0.247311828 + 0.09391259105 Combine like terms: 0.247311828 + 0.09391259105 = 0.34122441905 0.09391259105 + 0.6129032258x + x2 = 0.34122441905 Factor a perfect square on the left side: (x + 0.3064516129)(x + 0.3064516129) = 0.34122441905 Calculate the square root of the right side: 0.584144177 Break this problem into two subproblems by setting (x + 0.3064516129) equal to 0.584144177 and -0.584144177.Subproblem 1
x + 0.3064516129 = 0.584144177 Simplifying x + 0.3064516129 = 0.584144177 Reorder the terms: 0.3064516129 + x = 0.584144177 Solving 0.3064516129 + x = 0.584144177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3064516129' to each side of the equation. 0.3064516129 + -0.3064516129 + x = 0.584144177 + -0.3064516129 Combine like terms: 0.3064516129 + -0.3064516129 = 0.0000000000 0.0000000000 + x = 0.584144177 + -0.3064516129 x = 0.584144177 + -0.3064516129 Combine like terms: 0.584144177 + -0.3064516129 = 0.2776925641 x = 0.2776925641 Simplifying x = 0.2776925641Subproblem 2
x + 0.3064516129 = -0.584144177 Simplifying x + 0.3064516129 = -0.584144177 Reorder the terms: 0.3064516129 + x = -0.584144177 Solving 0.3064516129 + x = -0.584144177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3064516129' to each side of the equation. 0.3064516129 + -0.3064516129 + x = -0.584144177 + -0.3064516129 Combine like terms: 0.3064516129 + -0.3064516129 = 0.0000000000 0.0000000000 + x = -0.584144177 + -0.3064516129 x = -0.584144177 + -0.3064516129 Combine like terms: -0.584144177 + -0.3064516129 = -0.8905957899 x = -0.8905957899 Simplifying x = -0.8905957899Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2776925641, -0.8905957899}
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