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Simplifying 4.6x2 + 92x + 400 = 0 Reorder the terms: 400 + 92x + 4.6x2 = 0 Solving 400 + 92x + 4.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.6 the coefficient of the squared term: Divide each side by '4.6'. 86.95652174 + 20x + x2 = 0 Move the constant term to the right: Add '-86.95652174' to each side of the equation. 86.95652174 + 20x + -86.95652174 + x2 = 0 + -86.95652174 Reorder the terms: 86.95652174 + -86.95652174 + 20x + x2 = 0 + -86.95652174 Combine like terms: 86.95652174 + -86.95652174 = 0.00000000 0.00000000 + 20x + x2 = 0 + -86.95652174 20x + x2 = 0 + -86.95652174 Combine like terms: 0 + -86.95652174 = -86.95652174 20x + x2 = -86.95652174 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -86.95652174 + 100 Reorder the terms: 100 + 20x + x2 = -86.95652174 + 100 Combine like terms: -86.95652174 + 100 = 13.04347826 100 + 20x + x2 = 13.04347826 Factor a perfect square on the left side: (x + 10)(x + 10) = 13.04347826 Calculate the square root of the right side: 3.611575592 Break this problem into two subproblems by setting (x + 10) equal to 3.611575592 and -3.611575592.Subproblem 1
x + 10 = 3.611575592 Simplifying x + 10 = 3.611575592 Reorder the terms: 10 + x = 3.611575592 Solving 10 + x = 3.611575592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 3.611575592 + -10 Combine like terms: 10 + -10 = 0 0 + x = 3.611575592 + -10 x = 3.611575592 + -10 Combine like terms: 3.611575592 + -10 = -6.388424408 x = -6.388424408 Simplifying x = -6.388424408Subproblem 2
x + 10 = -3.611575592 Simplifying x + 10 = -3.611575592 Reorder the terms: 10 + x = -3.611575592 Solving 10 + x = -3.611575592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -3.611575592 + -10 Combine like terms: 10 + -10 = 0 0 + x = -3.611575592 + -10 x = -3.611575592 + -10 Combine like terms: -3.611575592 + -10 = -13.611575592 x = -13.611575592 Simplifying x = -13.611575592Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.388424408, -13.611575592}
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