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Simplifying 8x2 + -41x + 44 = 0 Reorder the terms: 44 + -41x + 8x2 = 0 Solving 44 + -41x + 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 + -5.125x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -5.125x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -5.125x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -5.125x + x2 = 0 + -5.5 -5.125x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -5.125x + x2 = -5.5 The x term is -5.125x. Take half its coefficient (-2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. -5.125x + 6.56640625 + x2 = -5.5 + 6.56640625 Reorder the terms: 6.56640625 + -5.125x + x2 = -5.5 + 6.56640625 Combine like terms: -5.5 + 6.56640625 = 1.06640625 6.56640625 + -5.125x + x2 = 1.06640625 Factor a perfect square on the left side: (x + -2.5625)(x + -2.5625) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (x + -2.5625) equal to 1.032669478 and -1.032669478.Subproblem 1
x + -2.5625 = 1.032669478 Simplifying x + -2.5625 = 1.032669478 Reorder the terms: -2.5625 + x = 1.032669478 Solving -2.5625 + x = 1.032669478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + x = 1.032669478 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = 1.032669478 + 2.5625 x = 1.032669478 + 2.5625 Combine like terms: 1.032669478 + 2.5625 = 3.595169478 x = 3.595169478 Simplifying x = 3.595169478Subproblem 2
x + -2.5625 = -1.032669478 Simplifying x + -2.5625 = -1.032669478 Reorder the terms: -2.5625 + x = -1.032669478 Solving -2.5625 + x = -1.032669478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + x = -1.032669478 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = -1.032669478 + 2.5625 x = -1.032669478 + 2.5625 Combine like terms: -1.032669478 + 2.5625 = 1.529830522 x = 1.529830522 Simplifying x = 1.529830522Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.595169478, 1.529830522}
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