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Simplifying 2x4 + -10x2 + 5 = 0 Reorder the terms: 5 + -10x2 + 2x4 = 0 Solving 5 + -10x2 + 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'. 2.5 + -5x2 + x4 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5x2 + -2.5 + x4 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5x2 + x4 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5x2 + x4 = 0 + -2.5 -5x2 + x4 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5x2 + x4 = -2.5 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -2.5 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + -5x2 + x4 = 3.75 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x2 + -2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x2 + -2.5 = 1.936491673 Simplifying x2 + -2.5 = 1.936491673 Reorder the terms: -2.5 + x2 = 1.936491673 Solving -2.5 + x2 = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 1.936491673 + 2.5 x2 = 1.936491673 + 2.5 Combine like terms: 1.936491673 + 2.5 = 4.436491673 x2 = 4.436491673 Simplifying x2 = 4.436491673 Take the square root of each side: x = {-2.106298097, 2.106298097}Subproblem 2
x2 + -2.5 = -1.936491673 Simplifying x2 + -2.5 = -1.936491673 Reorder the terms: -2.5 + x2 = -1.936491673 Solving -2.5 + x2 = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -1.936491673 + 2.5 x2 = -1.936491673 + 2.5 Combine like terms: -1.936491673 + 2.5 = 0.563508327 x2 = 0.563508327 Simplifying x2 = 0.563508327 Take the square root of each side: x = {-0.750671917, 0.750671917}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.106298097, 2.106298097, -0.750671917, 0.750671917}
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