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Simplifying 14x4 + -33x2 + 14 = 0 Reorder the terms: 14 + -33x2 + 14x4 = 0 Solving 14 + -33x2 + 14x4 = 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'. 1 + -2.357142857x2 + x4 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.357142857x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -2.357142857x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.357142857x2 + x4 = 0 + -1 -2.357142857x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.357142857x2 + x4 = -1 The x term is -2.357142857x2. Take half its coefficient (-1.178571429). Square it (1.389030613) and add it to both sides. Add '1.389030613' to each side of the equation. -2.357142857x2 + 1.389030613 + x4 = -1 + 1.389030613 Reorder the terms: 1.389030613 + -2.357142857x2 + x4 = -1 + 1.389030613 Combine like terms: -1 + 1.389030613 = 0.389030613 1.389030613 + -2.357142857x2 + x4 = 0.389030613 Factor a perfect square on the left side: (x2 + -1.178571429)(x2 + -1.178571429) = 0.389030613 Calculate the square root of the right side: 0.623723186 Break this problem into two subproblems by setting (x2 + -1.178571429) equal to 0.623723186 and -0.623723186.Subproblem 1
x2 + -1.178571429 = 0.623723186 Simplifying x2 + -1.178571429 = 0.623723186 Reorder the terms: -1.178571429 + x2 = 0.623723186 Solving -1.178571429 + x2 = 0.623723186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.178571429' to each side of the equation. -1.178571429 + 1.178571429 + x2 = 0.623723186 + 1.178571429 Combine like terms: -1.178571429 + 1.178571429 = 0.000000000 0.000000000 + x2 = 0.623723186 + 1.178571429 x2 = 0.623723186 + 1.178571429 Combine like terms: 0.623723186 + 1.178571429 = 1.802294615 x2 = 1.802294615 Simplifying x2 = 1.802294615 Take the square root of each side: x = {-1.342495667, 1.342495667}Subproblem 2
x2 + -1.178571429 = -0.623723186 Simplifying x2 + -1.178571429 = -0.623723186 Reorder the terms: -1.178571429 + x2 = -0.623723186 Solving -1.178571429 + x2 = -0.623723186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.178571429' to each side of the equation. -1.178571429 + 1.178571429 + x2 = -0.623723186 + 1.178571429 Combine like terms: -1.178571429 + 1.178571429 = 0.000000000 0.000000000 + x2 = -0.623723186 + 1.178571429 x2 = -0.623723186 + 1.178571429 Combine like terms: -0.623723186 + 1.178571429 = 0.554848243 x2 = 0.554848243 Simplifying x2 = 0.554848243 Take the square root of each side: x = {-0.744881362, 0.744881362}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.342495667, 1.342495667, -0.744881362, 0.744881362}
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