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Simplifying 10x2 + 32x4 + 6x3 = 0 Reorder the terms: 10x2 + 6x3 + 32x4 = 0 Solving 10x2 + 6x3 + 32x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(5 + 3x + 16x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(5 + 3x + 16x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 16x2 = 0 Solving 5 + 3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + 0.1875x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 0.1875x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 0.1875x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 0.1875x + x2 = 0 + -0.3125 0.1875x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 0.1875x + x2 = -0.3125 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = -0.3125 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = -0.3125 + 0.0087890625 Combine like terms: -0.3125 + 0.0087890625 = -0.3037109375 0.0087890625 + 0.1875x + x2 = -0.3037109375 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = -0.3037109375 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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