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Simplifying 14x2 + -4x + -6 = 0 Reorder the terms: -6 + -4x + 14x2 = 0 Solving -6 + -4x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -2x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2x + 7x2)' equal to zero and attempt to solve: Simplifying -3 + -2x + 7x2 = 0 Solving -3 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.2857142857x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.2857142857x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.4285714286 -0.2857142857x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.2857142857x + x2 = 0.4285714286 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.4285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.4285714286 + 0.02040816328 Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188 0.02040816328 + -0.2857142857x + x2 = 0.44897959188 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.44897959188 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.670059394 and -0.670059394.Subproblem 1
x + -0.1428571429 = 0.670059394 Simplifying x + -0.1428571429 = 0.670059394 Reorder the terms: -0.1428571429 + x = 0.670059394 Solving -0.1428571429 + x = 0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.670059394 + 0.1428571429 x = 0.670059394 + 0.1428571429 Combine like terms: 0.670059394 + 0.1428571429 = 0.8129165369 x = 0.8129165369 Simplifying x = 0.8129165369Subproblem 2
x + -0.1428571429 = -0.670059394 Simplifying x + -0.1428571429 = -0.670059394 Reorder the terms: -0.1428571429 + x = -0.670059394 Solving -0.1428571429 + x = -0.670059394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.670059394 + 0.1428571429 x = -0.670059394 + 0.1428571429 Combine like terms: -0.670059394 + 0.1428571429 = -0.5272022511 x = -0.5272022511 Simplifying x = -0.5272022511Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8129165369, -0.5272022511}Solution
x = {0.8129165369, -0.5272022511}
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