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Simplifying -4x2(3x3 + 8x + -9x2) = 0 Reorder the terms: -4x2(8x + -9x2 + 3x3) = 0 (8x * -4x2 + -9x2 * -4x2 + 3x3 * -4x2) = 0 (-32x3 + 36x4 + -12x5) = 0 Solving -32x3 + 36x4 + -12x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x3'. 4x3(-8 + 9x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(-8 + 9x + -3x2)' equal to zero and attempt to solve: Simplifying -8 + 9x + -3x2 = 0 Solving -8 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.666666667 + -3x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -3x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -3x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + -2.666666667 -3x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -3x + x2 = -2.666666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.666666667 + 2.25 Combine like terms: -2.666666667 + 2.25 = -0.416666667 2.25 + -3x + x2 = -0.416666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -0.416666667 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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