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Simplifying 4x7 + 28x6 + 80x5 = 0 Reorder the terms: 80x5 + 28x6 + 4x7 = 0 Solving 80x5 + 28x6 + 4x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x5'. 4x5(20 + 7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 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 '(20 + 7x + x2)' equal to zero and attempt to solve: Simplifying 20 + 7x + x2 = 0 Solving 20 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 7x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 7x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 7x + x2 = 0 + -20 7x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 7x + x2 = -20 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 = -20 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -20 + 12.25 Combine like terms: -20 + 12.25 = -7.75 12.25 + 7x + x2 = -7.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -7.75 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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