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Simplifying 62x2 + 44x + 5 = 0 Reorder the terms: 5 + 44x + 62x2 = 0 Solving 5 + 44x + 62x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 62 the coefficient of the squared term: Divide each side by '62'. 0.08064516129 + 0.7096774194x + x2 = 0 Move the constant term to the right: Add '-0.08064516129' to each side of the equation. 0.08064516129 + 0.7096774194x + -0.08064516129 + x2 = 0 + -0.08064516129 Reorder the terms: 0.08064516129 + -0.08064516129 + 0.7096774194x + x2 = 0 + -0.08064516129 Combine like terms: 0.08064516129 + -0.08064516129 = 0.00000000000 0.00000000000 + 0.7096774194x + x2 = 0 + -0.08064516129 0.7096774194x + x2 = 0 + -0.08064516129 Combine like terms: 0 + -0.08064516129 = -0.08064516129 0.7096774194x + x2 = -0.08064516129 The x term is 0.7096774194x. Take half its coefficient (0.3548387097). Square it (0.1259105099) and add it to both sides. Add '0.1259105099' to each side of the equation. 0.7096774194x + 0.1259105099 + x2 = -0.08064516129 + 0.1259105099 Reorder the terms: 0.1259105099 + 0.7096774194x + x2 = -0.08064516129 + 0.1259105099 Combine like terms: -0.08064516129 + 0.1259105099 = 0.04526534861 0.1259105099 + 0.7096774194x + x2 = 0.04526534861 Factor a perfect square on the left side: (x + 0.3548387097)(x + 0.3548387097) = 0.04526534861 Calculate the square root of the right side: 0.212756548 Break this problem into two subproblems by setting (x + 0.3548387097) equal to 0.212756548 and -0.212756548.Subproblem 1
x + 0.3548387097 = 0.212756548 Simplifying x + 0.3548387097 = 0.212756548 Reorder the terms: 0.3548387097 + x = 0.212756548 Solving 0.3548387097 + x = 0.212756548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3548387097' to each side of the equation. 0.3548387097 + -0.3548387097 + x = 0.212756548 + -0.3548387097 Combine like terms: 0.3548387097 + -0.3548387097 = 0.0000000000 0.0000000000 + x = 0.212756548 + -0.3548387097 x = 0.212756548 + -0.3548387097 Combine like terms: 0.212756548 + -0.3548387097 = -0.1420821617 x = -0.1420821617 Simplifying x = -0.1420821617Subproblem 2
x + 0.3548387097 = -0.212756548 Simplifying x + 0.3548387097 = -0.212756548 Reorder the terms: 0.3548387097 + x = -0.212756548 Solving 0.3548387097 + x = -0.212756548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3548387097' to each side of the equation. 0.3548387097 + -0.3548387097 + x = -0.212756548 + -0.3548387097 Combine like terms: 0.3548387097 + -0.3548387097 = 0.0000000000 0.0000000000 + x = -0.212756548 + -0.3548387097 x = -0.212756548 + -0.3548387097 Combine like terms: -0.212756548 + -0.3548387097 = -0.5675952577 x = -0.5675952577 Simplifying x = -0.5675952577Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1420821617, -0.5675952577}
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