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Simplifying x4 + -19x2 + -48 = 0 Reorder the terms: -48 + -19x2 + x4 = 0 Solving -48 + -19x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -19x2 + 48 + x4 = 0 + 48 Reorder the terms: -48 + 48 + -19x2 + x4 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -19x2 + x4 = 0 + 48 -19x2 + x4 = 0 + 48 Combine like terms: 0 + 48 = 48 -19x2 + x4 = 48 The x term is -19x2. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x2 + 90.25 + x4 = 48 + 90.25 Reorder the terms: 90.25 + -19x2 + x4 = 48 + 90.25 Combine like terms: 48 + 90.25 = 138.25 90.25 + -19x2 + x4 = 138.25 Factor a perfect square on the left side: (x2 + -9.5)(x2 + -9.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x2 + -9.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x2 + -9.5 = 11.757976016 Simplifying x2 + -9.5 = 11.757976016 Reorder the terms: -9.5 + x2 = 11.757976016 Solving -9.5 + x2 = 11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x2 = 11.757976016 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x2 = 11.757976016 + 9.5 x2 = 11.757976016 + 9.5 Combine like terms: 11.757976016 + 9.5 = 21.257976016 x2 = 21.257976016 Simplifying x2 = 21.257976016 Take the square root of each side: x = {-4.610637268, 4.610637268}Subproblem 2
x2 + -9.5 = -11.757976016 Simplifying x2 + -9.5 = -11.757976016 Reorder the terms: -9.5 + x2 = -11.757976016 Solving -9.5 + x2 = -11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x2 = -11.757976016 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x2 = -11.757976016 + 9.5 x2 = -11.757976016 + 9.5 Combine like terms: -11.757976016 + 9.5 = -2.257976016 x2 = -2.257976016 Simplifying x2 = -2.257976016 Reorder the terms: 2.257976016 + x2 = -2.257976016 + 2.257976016 Combine like terms: -2.257976016 + 2.257976016 = 0.000000000 2.257976016 + 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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