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Simplifying 4x6 + -28x5 + 68x4 = 0 Reorder the terms: 68x4 + -28x5 + 4x6 = 0 Solving 68x4 + -28x5 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x4'. 4x4(17 + -7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(17 + -7x + x2)' equal to zero and attempt to solve: Simplifying 17 + -7x + x2 = 0 Solving 17 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -7x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -7x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -7x + x2 = 0 + -17 -7x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -7x + x2 = -17 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -17 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -17 + 12.25 Combine like terms: -17 + 12.25 = -4.75 12.25 + -7x + x2 = -4.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -4.75 Can't calculate square root of the right side. 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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