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Simplifying X = -7X2 + 3X + 3 Reorder the terms: X = 3 + 3X + -7X2 Solving X = 3 + 3X + -7X2 Solving for variable 'X'. Reorder the terms: -3 + X + -3X + 7X2 = 3 + 3X + -7X2 + -3 + -3X + 7X2 Combine like terms: X + -3X = -2X -3 + -2X + 7X2 = 3 + 3X + -7X2 + -3 + -3X + 7X2 Reorder the terms: -3 + -2X + 7X2 = 3 + -3 + 3X + -3X + -7X2 + 7X2 Combine like terms: 3 + -3 = 0 -3 + -2X + 7X2 = 0 + 3X + -3X + -7X2 + 7X2 -3 + -2X + 7X2 = 3X + -3X + -7X2 + 7X2 Combine like terms: 3X + -3X = 0 -3 + -2X + 7X2 = 0 + -7X2 + 7X2 -3 + -2X + 7X2 = -7X2 + 7X2 Combine like terms: -7X2 + 7X2 = 0 -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}
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