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Simplifying 10x6 + -9x5 + 16x4 = 0 Reorder the terms: 16x4 + -9x5 + 10x6 = 0 Solving 16x4 + -9x5 + 10x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(16 + -9x + 10x2) = 0Subproblem 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 '(16 + -9x + 10x2)' equal to zero and attempt to solve: Simplifying 16 + -9x + 10x2 = 0 Solving 16 + -9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.6 + -0.9x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -0.9x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -0.9x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -0.9x + x2 = 0 + -1.6 -0.9x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -0.9x + x2 = -1.6 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = -1.6 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = -1.6 + 0.2025 Combine like terms: -1.6 + 0.2025 = -1.3975 0.2025 + -0.9x + x2 = -1.3975 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = -1.3975 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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