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Simplifying x2 + 39x + -44 = 0 Reorder the terms: -44 + 39x + x2 = 0 Solving -44 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 39x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 39x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 39x + x2 = 0 + 44 39x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 39x + x2 = 44 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = 44 + 380.25 Reorder the terms: 380.25 + 39x + x2 = 44 + 380.25 Combine like terms: 44 + 380.25 = 424.25 380.25 + 39x + x2 = 424.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 424.25 Calculate the square root of the right side: 20.597329924 Break this problem into two subproblems by setting (x + 19.5) equal to 20.597329924 and -20.597329924.Subproblem 1
x + 19.5 = 20.597329924 Simplifying x + 19.5 = 20.597329924 Reorder the terms: 19.5 + x = 20.597329924 Solving 19.5 + x = 20.597329924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 20.597329924 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 20.597329924 + -19.5 x = 20.597329924 + -19.5 Combine like terms: 20.597329924 + -19.5 = 1.097329924 x = 1.097329924 Simplifying x = 1.097329924Subproblem 2
x + 19.5 = -20.597329924 Simplifying x + 19.5 = -20.597329924 Reorder the terms: 19.5 + x = -20.597329924 Solving 19.5 + x = -20.597329924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -20.597329924 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -20.597329924 + -19.5 x = -20.597329924 + -19.5 Combine like terms: -20.597329924 + -19.5 = -40.097329924 x = -40.097329924 Simplifying x = -40.097329924Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.097329924, -40.097329924}
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