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Simplifying x4 + -10x2 + -79 = 0 Reorder the terms: -79 + -10x2 + x4 = 0 Solving -79 + -10x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -10x2 + 79 + x4 = 0 + 79 Reorder the terms: -79 + 79 + -10x2 + x4 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -10x2 + x4 = 0 + 79 -10x2 + x4 = 0 + 79 Combine like terms: 0 + 79 = 79 -10x2 + x4 = 79 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 = 79 + 25 Reorder the terms: 25 + -10x2 + x4 = 79 + 25 Combine like terms: 79 + 25 = 104 25 + -10x2 + x4 = 104 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x2 + -5) equal to 10.198039027 and -10.198039027.Subproblem 1
x2 + -5 = 10.198039027 Simplifying x2 + -5 = 10.198039027 Reorder the terms: -5 + x2 = 10.198039027 Solving -5 + x2 = 10.198039027 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 = 10.198039027 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 10.198039027 + 5 x2 = 10.198039027 + 5 Combine like terms: 10.198039027 + 5 = 15.198039027 x2 = 15.198039027 Simplifying x2 = 15.198039027 Take the square root of each side: x = {-3.89846624, 3.89846624}Subproblem 2
x2 + -5 = -10.198039027 Simplifying x2 + -5 = -10.198039027 Reorder the terms: -5 + x2 = -10.198039027 Solving -5 + x2 = -10.198039027 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 = -10.198039027 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -10.198039027 + 5 x2 = -10.198039027 + 5 Combine like terms: -10.198039027 + 5 = -5.198039027 x2 = -5.198039027 Simplifying x2 = -5.198039027 Reorder the terms: 5.198039027 + x2 = -5.198039027 + 5.198039027 Combine like terms: -5.198039027 + 5.198039027 = 0.000000000 5.198039027 + 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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