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Simplifying x4 + 28x2 + -4 = 0 Reorder the terms: -4 + 28x2 + x4 = 0 Solving -4 + 28x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 28x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + 28x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 28x2 + x4 = 0 + 4 28x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 28x2 + x4 = 4 The x term is 28x2. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x2 + 196 + x4 = 4 + 196 Reorder the terms: 196 + 28x2 + x4 = 4 + 196 Combine like terms: 4 + 196 = 200 196 + 28x2 + x4 = 200 Factor a perfect square on the left side: (x2 + 14)(x2 + 14) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x2 + 14) equal to 14.142135624 and -14.142135624.Subproblem 1
x2 + 14 = 14.142135624 Simplifying x2 + 14 = 14.142135624 Reorder the terms: 14 + x2 = 14.142135624 Solving 14 + x2 = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = 14.142135624 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = 14.142135624 + -14 x2 = 14.142135624 + -14 Combine like terms: 14.142135624 + -14 = 0.142135624 x2 = 0.142135624 Simplifying x2 = 0.142135624 Take the square root of each side: x = {-0.377008785, 0.377008785}Subproblem 2
x2 + 14 = -14.142135624 Simplifying x2 + 14 = -14.142135624 Reorder the terms: 14 + x2 = -14.142135624 Solving 14 + x2 = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = -14.142135624 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = -14.142135624 + -14 x2 = -14.142135624 + -14 Combine like terms: -14.142135624 + -14 = -28.142135624 x2 = -28.142135624 Simplifying x2 = -28.142135624 Reorder the terms: 28.142135624 + x2 = -28.142135624 + 28.142135624 Combine like terms: -28.142135624 + 28.142135624 = 0.000000000 28.142135624 + x2 = 0.000000000 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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