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Simplifying x4 + 30x2 + 100 = 0 Reorder the terms: 100 + 30x2 + x4 = 0 Solving 100 + 30x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 30x2 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + 30x2 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 30x2 + x4 = 0 + -100 30x2 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 30x2 + x4 = -100 The x term is 30x2. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x2 + 225 + x4 = -100 + 225 Reorder the terms: 225 + 30x2 + x4 = -100 + 225 Combine like terms: -100 + 225 = 125 225 + 30x2 + x4 = 125 Factor a perfect square on the left side: (x2 + 15)(x2 + 15) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x2 + 15) equal to 11.180339887 and -11.180339887.Subproblem 1
x2 + 15 = 11.180339887 Simplifying x2 + 15 = 11.180339887 Reorder the terms: 15 + x2 = 11.180339887 Solving 15 + x2 = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x2 = 11.180339887 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = 11.180339887 + -15 x2 = 11.180339887 + -15 Combine like terms: 11.180339887 + -15 = -3.819660113 x2 = -3.819660113 Simplifying x2 = -3.819660113 Reorder the terms: 3.819660113 + x2 = -3.819660113 + 3.819660113 Combine like terms: -3.819660113 + 3.819660113 = 0.000000000 3.819660113 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 15 = -11.180339887 Simplifying x2 + 15 = -11.180339887 Reorder the terms: 15 + x2 = -11.180339887 Solving 15 + x2 = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x2 = -11.180339887 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = -11.180339887 + -15 x2 = -11.180339887 + -15 Combine like terms: -11.180339887 + -15 = -26.180339887 x2 = -26.180339887 Simplifying x2 = -26.180339887 Reorder the terms: 26.180339887 + x2 = -26.180339887 + 26.180339887 Combine like terms: -26.180339887 + 26.180339887 = 0.000000000 26.180339887 + 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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