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Simplifying 14x2 + -5x + -8 = 0 Reorder the terms: -8 + -5x + 14x2 = 0 Solving -8 + -5x + 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'. -0.5714285714 + -0.3571428571x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.3571428571x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.3571428571x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.3571428571x + x2 = 0 + 0.5714285714 -0.3571428571x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.3571428571x + x2 = 0.5714285714 The x term is -0.3571428571x. Take half its coefficient (-0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. -0.3571428571x + 0.03188775511 + x2 = 0.5714285714 + 0.03188775511 Reorder the terms: 0.03188775511 + -0.3571428571x + x2 = 0.5714285714 + 0.03188775511 Combine like terms: 0.5714285714 + 0.03188775511 = 0.60331632651 0.03188775511 + -0.3571428571x + x2 = 0.60331632651 Factor a perfect square on the left side: (x + -0.1785714286)(x + -0.1785714286) = 0.60331632651 Calculate the square root of the right side: 0.776734399 Break this problem into two subproblems by setting (x + -0.1785714286) equal to 0.776734399 and -0.776734399.Subproblem 1
x + -0.1785714286 = 0.776734399 Simplifying x + -0.1785714286 = 0.776734399 Reorder the terms: -0.1785714286 + x = 0.776734399 Solving -0.1785714286 + x = 0.776734399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = 0.776734399 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = 0.776734399 + 0.1785714286 x = 0.776734399 + 0.1785714286 Combine like terms: 0.776734399 + 0.1785714286 = 0.9553058276 x = 0.9553058276 Simplifying x = 0.9553058276Subproblem 2
x + -0.1785714286 = -0.776734399 Simplifying x + -0.1785714286 = -0.776734399 Reorder the terms: -0.1785714286 + x = -0.776734399 Solving -0.1785714286 + x = -0.776734399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = -0.776734399 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = -0.776734399 + 0.1785714286 x = -0.776734399 + 0.1785714286 Combine like terms: -0.776734399 + 0.1785714286 = -0.5981629704 x = -0.5981629704 Simplifying x = -0.5981629704Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9553058276, -0.5981629704}
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