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Simplifying 14x2 + -23x + 6 = 0 Reorder the terms: 6 + -23x + 14x2 = 0 Solving 6 + -23x + 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'. 0.4285714286 + -1.642857143x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -1.642857143x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -1.642857143x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -1.642857143x + x2 = 0 + -0.4285714286 -1.642857143x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -1.642857143x + x2 = -0.4285714286 The x term is -1.642857143x. Take half its coefficient (-0.8214285715). Square it (0.6747448981) and add it to both sides. Add '0.6747448981' to each side of the equation. -1.642857143x + 0.6747448981 + x2 = -0.4285714286 + 0.6747448981 Reorder the terms: 0.6747448981 + -1.642857143x + x2 = -0.4285714286 + 0.6747448981 Combine like terms: -0.4285714286 + 0.6747448981 = 0.2461734695 0.6747448981 + -1.642857143x + x2 = 0.2461734695 Factor a perfect square on the left side: (x + -0.8214285715)(x + -0.8214285715) = 0.2461734695 Calculate the square root of the right side: 0.496158714 Break this problem into two subproblems by setting (x + -0.8214285715) equal to 0.496158714 and -0.496158714.Subproblem 1
x + -0.8214285715 = 0.496158714 Simplifying x + -0.8214285715 = 0.496158714 Reorder the terms: -0.8214285715 + x = 0.496158714 Solving -0.8214285715 + x = 0.496158714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = 0.496158714 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = 0.496158714 + 0.8214285715 x = 0.496158714 + 0.8214285715 Combine like terms: 0.496158714 + 0.8214285715 = 1.3175872855 x = 1.3175872855 Simplifying x = 1.3175872855Subproblem 2
x + -0.8214285715 = -0.496158714 Simplifying x + -0.8214285715 = -0.496158714 Reorder the terms: -0.8214285715 + x = -0.496158714 Solving -0.8214285715 + x = -0.496158714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = -0.496158714 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = -0.496158714 + 0.8214285715 x = -0.496158714 + 0.8214285715 Combine like terms: -0.496158714 + 0.8214285715 = 0.3252698575 x = 0.3252698575 Simplifying x = 0.3252698575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3175872855, 0.3252698575}
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