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Simplifying 14x2 + 3x + -12 = 0 Reorder the terms: -12 + 3x + 14x2 = 0 Solving -12 + 3x + 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'. -0.8571428571 + 0.2142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.2142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.2142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.2142857143x + x2 = 0 + 0.8571428571 0.2142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.2142857143x + x2 = 0.8571428571 The x term is 0.2142857143x. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143x + 0.01147959185 + x2 = 0.8571428571 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143x + x2 = 0.8571428571 + 0.01147959185 Combine like terms: 0.8571428571 + 0.01147959185 = 0.86862244895 0.01147959185 + 0.2142857143x + x2 = 0.86862244895 Factor a perfect square on the left side: (x + 0.1071428572)(x + 0.1071428572) = 0.86862244895 Calculate the square root of the right side: 0.931999168 Break this problem into two subproblems by setting (x + 0.1071428572) equal to 0.931999168 and -0.931999168.Subproblem 1
x + 0.1071428572 = 0.931999168 Simplifying x + 0.1071428572 = 0.931999168 Reorder the terms: 0.1071428572 + x = 0.931999168 Solving 0.1071428572 + x = 0.931999168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x = 0.931999168 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = 0.931999168 + -0.1071428572 x = 0.931999168 + -0.1071428572 Combine like terms: 0.931999168 + -0.1071428572 = 0.8248563108 x = 0.8248563108 Simplifying x = 0.8248563108Subproblem 2
x + 0.1071428572 = -0.931999168 Simplifying x + 0.1071428572 = -0.931999168 Reorder the terms: 0.1071428572 + x = -0.931999168 Solving 0.1071428572 + x = -0.931999168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x = -0.931999168 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = -0.931999168 + -0.1071428572 x = -0.931999168 + -0.1071428572 Combine like terms: -0.931999168 + -0.1071428572 = -1.0391420252 x = -1.0391420252 Simplifying x = -1.0391420252Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8248563108, -1.0391420252}
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