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Simplifying 14x2 + -50x + 27 = 0 Reorder the terms: 27 + -50x + 14x2 = 0 Solving 27 + -50x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.928571429 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '-1.928571429' to each side of the equation. 1.928571429 + -3.571428571x + -1.928571429 + x2 = 0 + -1.928571429 Reorder the terms: 1.928571429 + -1.928571429 + -3.571428571x + x2 = 0 + -1.928571429 Combine like terms: 1.928571429 + -1.928571429 = 0.000000000 0.000000000 + -3.571428571x + x2 = 0 + -1.928571429 -3.571428571x + x2 = 0 + -1.928571429 Combine like terms: 0 + -1.928571429 = -1.928571429 -3.571428571x + x2 = -1.928571429 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = -1.928571429 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = -1.928571429 + 3.188775511 Combine like terms: -1.928571429 + 3.188775511 = 1.260204082 3.188775511 + -3.571428571x + x2 = 1.260204082 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 1.260204082 Calculate the square root of the right side: 1.122588118 Break this problem into two subproblems by setting (x + -1.785714286) equal to 1.122588118 and -1.122588118.Subproblem 1
x + -1.785714286 = 1.122588118 Simplifying x + -1.785714286 = 1.122588118 Reorder the terms: -1.785714286 + x = 1.122588118 Solving -1.785714286 + x = 1.122588118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 1.122588118 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 1.122588118 + 1.785714286 x = 1.122588118 + 1.785714286 Combine like terms: 1.122588118 + 1.785714286 = 2.908302404 x = 2.908302404 Simplifying x = 2.908302404Subproblem 2
x + -1.785714286 = -1.122588118 Simplifying x + -1.785714286 = -1.122588118 Reorder the terms: -1.785714286 + x = -1.122588118 Solving -1.785714286 + x = -1.122588118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -1.122588118 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -1.122588118 + 1.785714286 x = -1.122588118 + 1.785714286 Combine like terms: -1.122588118 + 1.785714286 = 0.663126168 x = 0.663126168 Simplifying x = 0.663126168Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.908302404, 0.663126168}
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