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Simplifying 4x2 + -43x + 102 = 0 Reorder the terms: 102 + -43x + 4x2 = 0 Solving 102 + -43x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25.5 + -10.75x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + -10.75x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + -10.75x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + -10.75x + x2 = 0 + -25.5 -10.75x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 -10.75x + x2 = -25.5 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 = -25.5 + 28.890625 Reorder the terms: 28.890625 + -10.75x + x2 = -25.5 + 28.890625 Combine like terms: -25.5 + 28.890625 = 3.390625 28.890625 + -10.75x + x2 = 3.390625 Factor a perfect square on the left side: (x + -5.375)(x + -5.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -5.375) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -5.375 = 1.841364983 Simplifying x + -5.375 = 1.841364983 Reorder the terms: -5.375 + x = 1.841364983 Solving -5.375 + x = 1.841364983 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 = 1.841364983 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = 1.841364983 + 5.375 x = 1.841364983 + 5.375 Combine like terms: 1.841364983 + 5.375 = 7.216364983 x = 7.216364983 Simplifying x = 7.216364983Subproblem 2
x + -5.375 = -1.841364983 Simplifying x + -5.375 = -1.841364983 Reorder the terms: -5.375 + x = -1.841364983 Solving -5.375 + x = -1.841364983 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 = -1.841364983 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = -1.841364983 + 5.375 x = -1.841364983 + 5.375 Combine like terms: -1.841364983 + 5.375 = 3.533635017 x = 3.533635017 Simplifying x = 3.533635017Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.216364983, 3.533635017}
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