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Simplifying x4 + -10x2 + -3 = 0 Reorder the terms: -3 + -10x2 + x4 = 0 Solving -3 + -10x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -10x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + -10x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10x2 + x4 = 0 + 3 -10x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 -10x2 + x4 = 3 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = 3 + 25 Reorder the terms: 25 + -10x2 + x4 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + -10x2 + x4 = 28 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x2 + -5) equal to 5.291502622 and -5.291502622.Subproblem 1
x2 + -5 = 5.291502622 Simplifying x2 + -5 = 5.291502622 Reorder the terms: -5 + x2 = 5.291502622 Solving -5 + x2 = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 5.291502622 + 5 x2 = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 x2 = 10.291502622 Simplifying x2 = 10.291502622 Take the square root of each side: x = {-3.208037191, 3.208037191}Subproblem 2
x2 + -5 = -5.291502622 Simplifying x2 + -5 = -5.291502622 Reorder the terms: -5 + x2 = -5.291502622 Solving -5 + x2 = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -5.291502622 + 5 x2 = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 x2 = -0.291502622 Simplifying x2 = -0.291502622 Reorder the terms: 0.291502622 + x2 = -0.291502622 + 0.291502622 Combine like terms: -0.291502622 + 0.291502622 = 0.000000000 0.291502622 + 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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