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Simplifying 5x2 + -32x + -104 = 0 Reorder the terms: -104 + -32x + 5x2 = 0 Solving -104 + -32x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20.8 + -6.4x + x2 = 0 Move the constant term to the right: Add '20.8' to each side of the equation. -20.8 + -6.4x + 20.8 + x2 = 0 + 20.8 Reorder the terms: -20.8 + 20.8 + -6.4x + x2 = 0 + 20.8 Combine like terms: -20.8 + 20.8 = 0.0 0.0 + -6.4x + x2 = 0 + 20.8 -6.4x + x2 = 0 + 20.8 Combine like terms: 0 + 20.8 = 20.8 -6.4x + x2 = 20.8 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 20.8 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 20.8 + 10.24 Combine like terms: 20.8 + 10.24 = 31.04 10.24 + -6.4x + x2 = 31.04 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 31.04 Calculate the square root of the right side: 5.571355311 Break this problem into two subproblems by setting (x + -3.2) equal to 5.571355311 and -5.571355311.Subproblem 1
x + -3.2 = 5.571355311 Simplifying x + -3.2 = 5.571355311 Reorder the terms: -3.2 + x = 5.571355311 Solving -3.2 + x = 5.571355311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 5.571355311 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 5.571355311 + 3.2 x = 5.571355311 + 3.2 Combine like terms: 5.571355311 + 3.2 = 8.771355311 x = 8.771355311 Simplifying x = 8.771355311Subproblem 2
x + -3.2 = -5.571355311 Simplifying x + -3.2 = -5.571355311 Reorder the terms: -3.2 + x = -5.571355311 Solving -3.2 + x = -5.571355311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -5.571355311 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -5.571355311 + 3.2 x = -5.571355311 + 3.2 Combine like terms: -5.571355311 + 3.2 = -2.371355311 x = -2.371355311 Simplifying x = -2.371355311Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.771355311, -2.371355311}
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