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Simplifying x4 + 4x2 + -7 = 0 Reorder the terms: -7 + 4x2 + x4 = 0 Solving -7 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 4x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + 4x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x2 + x4 = 0 + 7 4x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 4x2 + x4 = 7 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 = 7 + 4 Reorder the terms: 4 + 4x2 + x4 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4x2 + x4 = 11 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x2 + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
x2 + 2 = 3.31662479 Simplifying x2 + 2 = 3.31662479 Reorder the terms: 2 + x2 = 3.31662479 Solving 2 + x2 = 3.31662479 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 = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 3.31662479 + -2 x2 = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 x2 = 1.31662479 Simplifying x2 = 1.31662479 Take the square root of each side: x = {-1.147442718, 1.147442718}Subproblem 2
x2 + 2 = -3.31662479 Simplifying x2 + 2 = -3.31662479 Reorder the terms: 2 + x2 = -3.31662479 Solving 2 + x2 = -3.31662479 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 = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -3.31662479 + -2 x2 = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 x2 = -5.31662479 Simplifying x2 = -5.31662479 Reorder the terms: 5.31662479 + x2 = -5.31662479 + 5.31662479 Combine like terms: -5.31662479 + 5.31662479 = 0.00000000 5.31662479 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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