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Simplifying 2x4 + -11x2 + 8 = 0 Reorder the terms: 8 + -11x2 + 2x4 = 0 Solving 8 + -11x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -5.5x2 + x4 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.5x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -5.5x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.5x2 + x4 = 0 + -4 -5.5x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.5x2 + x4 = -4 The x term is -5.5x2. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x2 + 7.5625 + x4 = -4 + 7.5625 Reorder the terms: 7.5625 + -5.5x2 + x4 = -4 + 7.5625 Combine like terms: -4 + 7.5625 = 3.5625 7.5625 + -5.5x2 + x4 = 3.5625 Factor a perfect square on the left side: (x2 + -2.75)(x2 + -2.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x2 + -2.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x2 + -2.75 = 1.887458609 Simplifying x2 + -2.75 = 1.887458609 Reorder the terms: -2.75 + x2 = 1.887458609 Solving -2.75 + x2 = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x2 = 1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x2 = 1.887458609 + 2.75 x2 = 1.887458609 + 2.75 Combine like terms: 1.887458609 + 2.75 = 4.637458609 x2 = 4.637458609 Simplifying x2 = 4.637458609 Take the square root of each side: x = {-2.153475936, 2.153475936}Subproblem 2
x2 + -2.75 = -1.887458609 Simplifying x2 + -2.75 = -1.887458609 Reorder the terms: -2.75 + x2 = -1.887458609 Solving -2.75 + x2 = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x2 = -1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x2 = -1.887458609 + 2.75 x2 = -1.887458609 + 2.75 Combine like terms: -1.887458609 + 2.75 = 0.862541391 x2 = 0.862541391 Simplifying x2 = 0.862541391 Take the square root of each side: x = {-0.928731065, 0.928731065}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.153475936, 2.153475936, -0.928731065, 0.928731065}
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