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Simplifying 19.6788x2 + -147.186x + 124.78 = 0 Reorder the terms: 124.78 + -147.186x + 19.6788x2 = 0 Solving 124.78 + -147.186x + 19.6788x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.6788 the coefficient of the squared term: Divide each side by '19.6788'. 6.340833791 + -7.479419477x + x2 = 0 Move the constant term to the right: Add '-6.340833791' to each side of the equation. 6.340833791 + -7.479419477x + -6.340833791 + x2 = 0 + -6.340833791 Reorder the terms: 6.340833791 + -6.340833791 + -7.479419477x + x2 = 0 + -6.340833791 Combine like terms: 6.340833791 + -6.340833791 = 0.000000000 0.000000000 + -7.479419477x + x2 = 0 + -6.340833791 -7.479419477x + x2 = 0 + -6.340833791 Combine like terms: 0 + -6.340833791 = -6.340833791 -7.479419477x + x2 = -6.340833791 The x term is -7.479419477x. Take half its coefficient (-3.739709739). Square it (13.98542893) and add it to both sides. Add '13.98542893' to each side of the equation. -7.479419477x + 13.98542893 + x2 = -6.340833791 + 13.98542893 Reorder the terms: 13.98542893 + -7.479419477x + x2 = -6.340833791 + 13.98542893 Combine like terms: -6.340833791 + 13.98542893 = 7.644595139 13.98542893 + -7.479419477x + x2 = 7.644595139 Factor a perfect square on the left side: (x + -3.739709739)(x + -3.739709739) = 7.644595139 Calculate the square root of the right side: 2.764886099 Break this problem into two subproblems by setting (x + -3.739709739) equal to 2.764886099 and -2.764886099.Subproblem 1
x + -3.739709739 = 2.764886099 Simplifying x + -3.739709739 = 2.764886099 Reorder the terms: -3.739709739 + x = 2.764886099 Solving -3.739709739 + x = 2.764886099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.739709739' to each side of the equation. -3.739709739 + 3.739709739 + x = 2.764886099 + 3.739709739 Combine like terms: -3.739709739 + 3.739709739 = 0.000000000 0.000000000 + x = 2.764886099 + 3.739709739 x = 2.764886099 + 3.739709739 Combine like terms: 2.764886099 + 3.739709739 = 6.504595838 x = 6.504595838 Simplifying x = 6.504595838Subproblem 2
x + -3.739709739 = -2.764886099 Simplifying x + -3.739709739 = -2.764886099 Reorder the terms: -3.739709739 + x = -2.764886099 Solving -3.739709739 + x = -2.764886099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.739709739' to each side of the equation. -3.739709739 + 3.739709739 + x = -2.764886099 + 3.739709739 Combine like terms: -3.739709739 + 3.739709739 = 0.000000000 0.000000000 + x = -2.764886099 + 3.739709739 x = -2.764886099 + 3.739709739 Combine like terms: -2.764886099 + 3.739709739 = 0.97482364 x = 0.97482364 Simplifying x = 0.97482364Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.504595838, 0.97482364}
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