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Simplifying 48x4 + -30x3 + 6x2 = 0 Reorder the terms: 6x2 + -30x3 + 48x4 = 0 Solving 6x2 + -30x3 + 48x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(1 + -5x + 8x2) = 0 Ignore the factor 6.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 '(1 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + 8x2 = 0 Solving 1 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -0.625x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.625x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.625x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.625x + x2 = 0 + -0.125 -0.625x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.625x + x2 = -0.125 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -0.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -0.125 + 0.09765625 Combine like terms: -0.125 + 0.09765625 = -0.02734375 0.09765625 + -0.625x + x2 = -0.02734375 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = -0.02734375 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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