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Simplifying 0.25x4 + -1x2 + 1 = 0 Reorder the terms: 1 + -1x2 + 0.25x4 = 0 Solving 1 + -1x2 + 0.25x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 4 + -4x2 + x4 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -4x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4x2 + x4 = 0 + -4 -4x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -4x2 + x4 = -4 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = -4 + 4 Reorder the terms: 4 + -4x2 + x4 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -4x2 + x4 = 0 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x2 + -2) equal to 0 and 0.Subproblem 1
x2 + -2 = 0 Simplifying x2 + -2 = 0 Reorder the terms: -2 + x2 = 0 Solving -2 + x2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 0 + 2 x2 = 0 + 2 Combine like terms: 0 + 2 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
x2 + -2 = 0 Simplifying x2 + -2 = 0 Reorder the terms: -2 + x2 = 0 Solving -2 + x2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 0 + 2 x2 = 0 + 2 Combine like terms: 0 + 2 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.414213562, 1.414213562, -1.414213562, 1.414213562}
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