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Simplifying 0 = 4x2 + 43x + -116 Reorder the terms: 0 = -116 + 43x + 4x2 Solving 0 = -116 + 43x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 116 = 116 116 + -43x + -4x2 = -116 + 43x + 4x2 + 116 + -43x + -4x2 Reorder the terms: 116 + -43x + -4x2 = -116 + 116 + 43x + -43x + 4x2 + -4x2 Combine like terms: -116 + 116 = 0 116 + -43x + -4x2 = 0 + 43x + -43x + 4x2 + -4x2 116 + -43x + -4x2 = 43x + -43x + 4x2 + -4x2 Combine like terms: 43x + -43x = 0 116 + -43x + -4x2 = 0 + 4x2 + -4x2 116 + -43x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 116 + -43x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -29 + 10.75x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 10.75x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 10.75x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 10.75x + x2 = 0 + 29 10.75x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 10.75x + x2 = 29 The x term is 10.75x. Take half its coefficient (5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. 10.75x + 28.890625 + x2 = 29 + 28.890625 Reorder the terms: 28.890625 + 10.75x + x2 = 29 + 28.890625 Combine like terms: 29 + 28.890625 = 57.890625 28.890625 + 10.75x + x2 = 57.890625 Factor a perfect square on the left side: (x + 5.375)(x + 5.375) = 57.890625 Calculate the square root of the right side: 7.608588897 Break this problem into two subproblems by setting (x + 5.375) equal to 7.608588897 and -7.608588897.Subproblem 1
x + 5.375 = 7.608588897 Simplifying x + 5.375 = 7.608588897 Reorder the terms: 5.375 + x = 7.608588897 Solving 5.375 + x = 7.608588897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = 7.608588897 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = 7.608588897 + -5.375 x = 7.608588897 + -5.375 Combine like terms: 7.608588897 + -5.375 = 2.233588897 x = 2.233588897 Simplifying x = 2.233588897Subproblem 2
x + 5.375 = -7.608588897 Simplifying x + 5.375 = -7.608588897 Reorder the terms: 5.375 + x = -7.608588897 Solving 5.375 + x = -7.608588897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = -7.608588897 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = -7.608588897 + -5.375 x = -7.608588897 + -5.375 Combine like terms: -7.608588897 + -5.375 = -12.983588897 x = -12.983588897 Simplifying x = -12.983588897Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.233588897, -12.983588897}
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