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Simplifying x4 + -7x2 + 2 = 0 Reorder the terms: 2 + -7x2 + x4 = 0 Solving 2 + -7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -7x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x2 + x4 = 0 + -2 -7x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -7x2 + x4 = -2 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = -2 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + -7x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + -3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + -3.5 = 3.201562119 Simplifying x2 + -3.5 = 3.201562119 Reorder the terms: -3.5 + x2 = 3.201562119 Solving -3.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 3.201562119 + 3.5 x2 = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 x2 = 6.701562119 Simplifying x2 = 6.701562119 Take the square root of each side: x = {-2.588737553, 2.588737553}Subproblem 2
x2 + -3.5 = -3.201562119 Simplifying x2 + -3.5 = -3.201562119 Reorder the terms: -3.5 + x2 = -3.201562119 Solving -3.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -3.201562119 + 3.5 x2 = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 x2 = 0.298437881 Simplifying x2 = 0.298437881 Take the square root of each side: x = {-0.546294683, 0.546294683}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.588737553, 2.588737553, -0.546294683, 0.546294683}
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