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Simplifying 0.4x2 + -29x + 44 = 0 Reorder the terms: 44 + -29x + 0.4x2 = 0 Solving 44 + -29x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 110 + -72.5x + x2 = 0 Move the constant term to the right: Add '-110' to each side of the equation. 110 + -72.5x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + -72.5x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -72.5x + x2 = 0 + -110 -72.5x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -72.5x + x2 = -110 The x term is -72.5x. Take half its coefficient (-36.25). Square it (1314.0625) and add it to both sides. Add '1314.0625' to each side of the equation. -72.5x + 1314.0625 + x2 = -110 + 1314.0625 Reorder the terms: 1314.0625 + -72.5x + x2 = -110 + 1314.0625 Combine like terms: -110 + 1314.0625 = 1204.0625 1314.0625 + -72.5x + x2 = 1204.0625 Factor a perfect square on the left side: (x + -36.25)(x + -36.25) = 1204.0625 Calculate the square root of the right side: 34.699603744 Break this problem into two subproblems by setting (x + -36.25) equal to 34.699603744 and -34.699603744.Subproblem 1
x + -36.25 = 34.699603744 Simplifying x + -36.25 = 34.699603744 Reorder the terms: -36.25 + x = 34.699603744 Solving -36.25 + x = 34.699603744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.25' to each side of the equation. -36.25 + 36.25 + x = 34.699603744 + 36.25 Combine like terms: -36.25 + 36.25 = 0.00 0.00 + x = 34.699603744 + 36.25 x = 34.699603744 + 36.25 Combine like terms: 34.699603744 + 36.25 = 70.949603744 x = 70.949603744 Simplifying x = 70.949603744Subproblem 2
x + -36.25 = -34.699603744 Simplifying x + -36.25 = -34.699603744 Reorder the terms: -36.25 + x = -34.699603744 Solving -36.25 + x = -34.699603744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.25' to each side of the equation. -36.25 + 36.25 + x = -34.699603744 + 36.25 Combine like terms: -36.25 + 36.25 = 0.00 0.00 + x = -34.699603744 + 36.25 x = -34.699603744 + 36.25 Combine like terms: -34.699603744 + 36.25 = 1.550396256 x = 1.550396256 Simplifying x = 1.550396256Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.949603744, 1.550396256}
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