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Simplifying 10x7 + 3x4 + x = 0 Reorder the terms: x + 3x4 + 10x7 = 0 Solving x + 3x4 + 10x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 3x3 + 10x6) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + 3x3 + 10x6)' equal to zero and attempt to solve: Simplifying 1 + 3x3 + 10x6 = 0 Solving 1 + 3x3 + 10x6 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 0.3x3 + x6 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 0.3x3 + -0.1 + x6 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 0.3x3 + x6 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.3x3 + x6 = 0 + -0.1 0.3x3 + x6 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 0.3x3 + x6 = -0.1 The x term is 0.3x3. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x3 + 0.0225 + x6 = -0.1 + 0.0225 Reorder the terms: 0.0225 + 0.3x3 + x6 = -0.1 + 0.0225 Combine like terms: -0.1 + 0.0225 = -0.0775 0.0225 + 0.3x3 + x6 = -0.0775 Factor a perfect square on the left side: (x3 + 0.15)(x3 + 0.15) = -0.0775 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.Solution
x = {0}
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