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Simplifying y6 + -3y3 + -2 = 0 Reorder the terms: -2 + -3y3 + y6 = 0 Solving -2 + -3y3 + y6 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3y3 + 2 + y6 = 0 + 2 Reorder the terms: -2 + 2 + -3y3 + y6 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3y3 + y6 = 0 + 2 -3y3 + y6 = 0 + 2 Combine like terms: 0 + 2 = 2 -3y3 + y6 = 2 The y term is -3y3. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y3 + 2.25 + y6 = 2 + 2.25 Reorder the terms: 2.25 + -3y3 + y6 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3y3 + y6 = 4.25 Factor a perfect square on the left side: (y3 + -1.5)(y3 + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y3 + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
y3 + -1.5 = 2.061552813 Simplifying y3 + -1.5 = 2.061552813 Reorder the terms: -1.5 + y3 = 2.061552813 Solving -1.5 + y3 = 2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y3 = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y3 = 2.061552813 + 1.5 y3 = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 y3 = 3.561552813 Simplifying y3 = 3.561552813 Reorder the terms: -3.561552813 + y3 = 3.561552813 + -3.561552813 Combine like terms: 3.561552813 + -3.561552813 = 0.000000000 -3.561552813 + y3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y3 + -1.5 = -2.061552813 Simplifying y3 + -1.5 = -2.061552813 Reorder the terms: -1.5 + y3 = -2.061552813 Solving -1.5 + y3 = -2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y3 = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y3 = -2.061552813 + 1.5 y3 = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 y3 = -0.561552813 Simplifying y3 = -0.561552813 Reorder the terms: 0.561552813 + y3 = -0.561552813 + 0.561552813 Combine like terms: -0.561552813 + 0.561552813 = 0.000000000 0.561552813 + y3 = 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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