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Simplifying x4 + -7x2 + -12 = 0 Reorder the terms: -12 + -7x2 + x4 = 0 Solving -12 + -7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -7x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + -7x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -7x2 + x4 = 0 + 12 -7x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 -7x2 + x4 = 12 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 = 12 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + -7x2 + x4 = 24.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x2 + -3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x2 + -3.5 = 4.924428901 Simplifying x2 + -3.5 = 4.924428901 Reorder the terms: -3.5 + x2 = 4.924428901 Solving -3.5 + x2 = 4.924428901 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 = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 4.924428901 + 3.5 x2 = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 x2 = 8.424428901 Simplifying x2 = 8.424428901 Take the square root of each side: x = {-2.902486675, 2.902486675}Subproblem 2
x2 + -3.5 = -4.924428901 Simplifying x2 + -3.5 = -4.924428901 Reorder the terms: -3.5 + x2 = -4.924428901 Solving -3.5 + x2 = -4.924428901 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 = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -4.924428901 + 3.5 x2 = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 x2 = -1.424428901 Simplifying x2 = -1.424428901 Reorder the terms: 1.424428901 + x2 = -1.424428901 + 1.424428901 Combine like terms: -1.424428901 + 1.424428901 = 0.000000000 1.424428901 + 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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