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Simplifying 2x4 + -16x2 + 1 = 0 Reorder the terms: 1 + -16x2 + 2x4 = 0 Solving 1 + -16x2 + 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'. 0.5 + -8x2 + x4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -8x2 + -0.5 + x4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -8x2 + x4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -8x2 + x4 = 0 + -0.5 -8x2 + x4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -8x2 + x4 = -0.5 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -0.5 + 16 Reorder the terms: 16 + -8x2 + x4 = -0.5 + 16 Combine like terms: -0.5 + 16 = 15.5 16 + -8x2 + x4 = 15.5 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (x2 + -4) equal to 3.937003937 and -3.937003937.Subproblem 1
x2 + -4 = 3.937003937 Simplifying x2 + -4 = 3.937003937 Reorder the terms: -4 + x2 = 3.937003937 Solving -4 + x2 = 3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 3.937003937 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.937003937 + 4 x2 = 3.937003937 + 4 Combine like terms: 3.937003937 + 4 = 7.937003937 x2 = 7.937003937 Simplifying x2 = 7.937003937 Take the square root of each side: x = {-2.817268879, 2.817268879}Subproblem 2
x2 + -4 = -3.937003937 Simplifying x2 + -4 = -3.937003937 Reorder the terms: -4 + x2 = -3.937003937 Solving -4 + x2 = -3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -3.937003937 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.937003937 + 4 x2 = -3.937003937 + 4 Combine like terms: -3.937003937 + 4 = 0.062996063 x2 = 0.062996063 Simplifying x2 = 0.062996063 Take the square root of each side: x = {-0.250990165, 0.250990165}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.817268879, 2.817268879, -0.250990165, 0.250990165}
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