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Simplifying 14x2 + 12x + -3 = 0 Reorder the terms: -3 + 12x + 14x2 = 0 Solving -3 + 12x + 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'. -0.2142857143 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.8571428571x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.8571428571x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + 0.2142857143 0.8571428571x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.8571428571x + x2 = 0.2142857143 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 0.2142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 0.2142857143 + 0.1836734694 Combine like terms: 0.2142857143 + 0.1836734694 = 0.3979591837 0.1836734694 + 0.8571428571x + x2 = 0.3979591837 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.3979591837 Calculate the square root of the right side: 0.630840062 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.630840062 and -0.630840062.Subproblem 1
x + 0.4285714286 = 0.630840062 Simplifying x + 0.4285714286 = 0.630840062 Reorder the terms: 0.4285714286 + x = 0.630840062 Solving 0.4285714286 + x = 0.630840062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.630840062 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.630840062 + -0.4285714286 x = 0.630840062 + -0.4285714286 Combine like terms: 0.630840062 + -0.4285714286 = 0.2022686334 x = 0.2022686334 Simplifying x = 0.2022686334Subproblem 2
x + 0.4285714286 = -0.630840062 Simplifying x + 0.4285714286 = -0.630840062 Reorder the terms: 0.4285714286 + x = -0.630840062 Solving 0.4285714286 + x = -0.630840062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.630840062 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.630840062 + -0.4285714286 x = -0.630840062 + -0.4285714286 Combine like terms: -0.630840062 + -0.4285714286 = -1.0594114906 x = -1.0594114906 Simplifying x = -1.0594114906Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2022686334, -1.0594114906}
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