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Simplifying 8x2 + -49x + 44 = 0 Reorder the terms: 44 + -49x + 8x2 = 0 Solving 44 + -49x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.5 + -6.125x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -6.125x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -6.125x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -6.125x + x2 = 0 + -5.5 -6.125x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -6.125x + x2 = -5.5 The x term is -6.125x. Take half its coefficient (-3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. -6.125x + 9.37890625 + x2 = -5.5 + 9.37890625 Reorder the terms: 9.37890625 + -6.125x + x2 = -5.5 + 9.37890625 Combine like terms: -5.5 + 9.37890625 = 3.87890625 9.37890625 + -6.125x + x2 = 3.87890625 Factor a perfect square on the left side: (x + -3.0625)(x + -3.0625) = 3.87890625 Calculate the square root of the right side: 1.969493907 Break this problem into two subproblems by setting (x + -3.0625) equal to 1.969493907 and -1.969493907.Subproblem 1
x + -3.0625 = 1.969493907 Simplifying x + -3.0625 = 1.969493907 Reorder the terms: -3.0625 + x = 1.969493907 Solving -3.0625 + x = 1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = 1.969493907 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = 1.969493907 + 3.0625 x = 1.969493907 + 3.0625 Combine like terms: 1.969493907 + 3.0625 = 5.031993907 x = 5.031993907 Simplifying x = 5.031993907Subproblem 2
x + -3.0625 = -1.969493907 Simplifying x + -3.0625 = -1.969493907 Reorder the terms: -3.0625 + x = -1.969493907 Solving -3.0625 + x = -1.969493907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = -1.969493907 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = -1.969493907 + 3.0625 x = -1.969493907 + 3.0625 Combine like terms: -1.969493907 + 3.0625 = 1.093006093 x = 1.093006093 Simplifying x = 1.093006093Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.031993907, 1.093006093}
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