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Simplifying 14x2 + 57x + 30 = 0 Reorder the terms: 30 + 57x + 14x2 = 0 Solving 30 + 57x + 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'. 2.142857143 + 4.071428571x + x2 = 0 Move the constant term to the right: Add '-2.142857143' to each side of the equation. 2.142857143 + 4.071428571x + -2.142857143 + x2 = 0 + -2.142857143 Reorder the terms: 2.142857143 + -2.142857143 + 4.071428571x + x2 = 0 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + 4.071428571x + x2 = 0 + -2.142857143 4.071428571x + x2 = 0 + -2.142857143 Combine like terms: 0 + -2.142857143 = -2.142857143 4.071428571x + x2 = -2.142857143 The x term is 4.071428571x. Take half its coefficient (2.035714286). Square it (4.144132654) and add it to both sides. Add '4.144132654' to each side of the equation. 4.071428571x + 4.144132654 + x2 = -2.142857143 + 4.144132654 Reorder the terms: 4.144132654 + 4.071428571x + x2 = -2.142857143 + 4.144132654 Combine like terms: -2.142857143 + 4.144132654 = 2.001275511 4.144132654 + 4.071428571x + x2 = 2.001275511 Factor a perfect square on the left side: (x + 2.035714286)(x + 2.035714286) = 2.001275511 Calculate the square root of the right side: 1.414664452 Break this problem into two subproblems by setting (x + 2.035714286) equal to 1.414664452 and -1.414664452.Subproblem 1
x + 2.035714286 = 1.414664452 Simplifying x + 2.035714286 = 1.414664452 Reorder the terms: 2.035714286 + x = 1.414664452 Solving 2.035714286 + x = 1.414664452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.035714286' to each side of the equation. 2.035714286 + -2.035714286 + x = 1.414664452 + -2.035714286 Combine like terms: 2.035714286 + -2.035714286 = 0.000000000 0.000000000 + x = 1.414664452 + -2.035714286 x = 1.414664452 + -2.035714286 Combine like terms: 1.414664452 + -2.035714286 = -0.621049834 x = -0.621049834 Simplifying x = -0.621049834Subproblem 2
x + 2.035714286 = -1.414664452 Simplifying x + 2.035714286 = -1.414664452 Reorder the terms: 2.035714286 + x = -1.414664452 Solving 2.035714286 + x = -1.414664452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.035714286' to each side of the equation. 2.035714286 + -2.035714286 + x = -1.414664452 + -2.035714286 Combine like terms: 2.035714286 + -2.035714286 = 0.000000000 0.000000000 + x = -1.414664452 + -2.035714286 x = -1.414664452 + -2.035714286 Combine like terms: -1.414664452 + -2.035714286 = -3.450378738 x = -3.450378738 Simplifying x = -3.450378738Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.621049834, -3.450378738}
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