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Simplifying 2.3x2 + -0.1x + -1.2 = 0 Reorder the terms: -1.2 + -0.1x + 2.3x2 = 0 Solving -1.2 + -0.1x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -0.5217391304 + -0.04347826087x + x2 = 0 Move the constant term to the right: Add '0.5217391304' to each side of the equation. -0.5217391304 + -0.04347826087x + 0.5217391304 + x2 = 0 + 0.5217391304 Reorder the terms: -0.5217391304 + 0.5217391304 + -0.04347826087x + x2 = 0 + 0.5217391304 Combine like terms: -0.5217391304 + 0.5217391304 = 0.0000000000 0.0000000000 + -0.04347826087x + x2 = 0 + 0.5217391304 -0.04347826087x + x2 = 0 + 0.5217391304 Combine like terms: 0 + 0.5217391304 = 0.5217391304 -0.04347826087x + x2 = 0.5217391304 The x term is -0.04347826087x. Take half its coefficient (-0.02173913044). Square it (0.0004725897923) and add it to both sides. Add '0.0004725897923' to each side of the equation. -0.04347826087x + 0.0004725897923 + x2 = 0.5217391304 + 0.0004725897923 Reorder the terms: 0.0004725897923 + -0.04347826087x + x2 = 0.5217391304 + 0.0004725897923 Combine like terms: 0.5217391304 + 0.0004725897923 = 0.5222117201923 0.0004725897923 + -0.04347826087x + x2 = 0.5222117201923 Factor a perfect square on the left side: (x + -0.02173913044)(x + -0.02173913044) = 0.5222117201923 Calculate the square root of the right side: 0.72264218 Break this problem into two subproblems by setting (x + -0.02173913044) equal to 0.72264218 and -0.72264218.Subproblem 1
x + -0.02173913044 = 0.72264218 Simplifying x + -0.02173913044 = 0.72264218 Reorder the terms: -0.02173913044 + x = 0.72264218 Solving -0.02173913044 + x = 0.72264218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02173913044' to each side of the equation. -0.02173913044 + 0.02173913044 + x = 0.72264218 + 0.02173913044 Combine like terms: -0.02173913044 + 0.02173913044 = 0.00000000000 0.00000000000 + x = 0.72264218 + 0.02173913044 x = 0.72264218 + 0.02173913044 Combine like terms: 0.72264218 + 0.02173913044 = 0.74438131044 x = 0.74438131044 Simplifying x = 0.74438131044Subproblem 2
x + -0.02173913044 = -0.72264218 Simplifying x + -0.02173913044 = -0.72264218 Reorder the terms: -0.02173913044 + x = -0.72264218 Solving -0.02173913044 + x = -0.72264218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02173913044' to each side of the equation. -0.02173913044 + 0.02173913044 + x = -0.72264218 + 0.02173913044 Combine like terms: -0.02173913044 + 0.02173913044 = 0.00000000000 0.00000000000 + x = -0.72264218 + 0.02173913044 x = -0.72264218 + 0.02173913044 Combine like terms: -0.72264218 + 0.02173913044 = -0.70090304956 x = -0.70090304956 Simplifying x = -0.70090304956Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.74438131044, -0.70090304956}
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