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Simplifying 2x4 + -26x2 + -72 = 0 Reorder the terms: -72 + -26x2 + 2x4 = 0 Solving -72 + -26x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -13x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + -13x2 + x4)' equal to zero and attempt to solve: Simplifying -36 + -13x2 + x4 = 0 Solving -36 + -13x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -13x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -13x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13x2 + x4 = 0 + 36 -13x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -13x2 + x4 = 36 The x term is -13x2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x2 + 42.25 + x4 = 36 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13x2 + x4 = 78.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x2 + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x2 + -6.5 = 8.845903006 Simplifying x2 + -6.5 = 8.845903006 Reorder the terms: -6.5 + x2 = 8.845903006 Solving -6.5 + x2 = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 8.845903006 + 6.5 x2 = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 x2 = 15.345903006 Simplifying x2 = 15.345903006 Take the square root of each side: x = {-3.917384715, 3.917384715}Subproblem 2
x2 + -6.5 = -8.845903006 Simplifying x2 + -6.5 = -8.845903006 Reorder the terms: -6.5 + x2 = -8.845903006 Solving -6.5 + x2 = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -8.845903006 + 6.5 x2 = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 x2 = -2.345903006 Simplifying x2 = -2.345903006 Reorder the terms: 2.345903006 + x2 = -2.345903006 + 2.345903006 Combine like terms: -2.345903006 + 2.345903006 = 0.000000000 2.345903006 + 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. 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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