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Simplifying -1x4 + -5x2 + 4 = 0 Reorder the terms: 4 + -5x2 + -1x4 = 0 Solving 4 + -5x2 + -1x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 5x2 + x4 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 5x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + 5x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x2 + x4 = 0 + 4 5x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 5x2 + x4 = 4 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = 4 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + 2.5 = 3.201562119 Simplifying x2 + 2.5 = 3.201562119 Reorder the terms: 2.5 + x2 = 3.201562119 Solving 2.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 3.201562119 + -2.5 x2 = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 x2 = 0.701562119 Simplifying x2 = 0.701562119 Take the square root of each side: x = {-0.837593051, 0.837593051}Subproblem 2
x2 + 2.5 = -3.201562119 Simplifying x2 + 2.5 = -3.201562119 Reorder the terms: 2.5 + x2 = -3.201562119 Solving 2.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -3.201562119 + -2.5 x2 = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 x2 = -5.701562119 Simplifying x2 = -5.701562119 Reorder the terms: 5.701562119 + x2 = -5.701562119 + 5.701562119 Combine like terms: -5.701562119 + 5.701562119 = 0.000000000 5.701562119 + 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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