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Simplifying 4x2 + -29x + 44 = 0 Reorder the terms: 44 + -29x + 4x2 = 0 Solving 44 + -29x + 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'. 11 + -7.25x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -7.25x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7.25x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7.25x + x2 = 0 + -11 -7.25x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7.25x + x2 = -11 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -11 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -11 + 13.140625 Combine like terms: -11 + 13.140625 = 2.140625 13.140625 + -7.25x + x2 = 2.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -3.625) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -3.625 = 1.463087489 Simplifying x + -3.625 = 1.463087489 Reorder the terms: -3.625 + x = 1.463087489 Solving -3.625 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 1.463087489 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 1.463087489 + 3.625 x = 1.463087489 + 3.625 Combine like terms: 1.463087489 + 3.625 = 5.088087489 x = 5.088087489 Simplifying x = 5.088087489Subproblem 2
x + -3.625 = -1.463087489 Simplifying x + -3.625 = -1.463087489 Reorder the terms: -3.625 + x = -1.463087489 Solving -3.625 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -1.463087489 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -1.463087489 + 3.625 x = -1.463087489 + 3.625 Combine like terms: -1.463087489 + 3.625 = 2.161912511 x = 2.161912511 Simplifying x = 2.161912511Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.088087489, 2.161912511}
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