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Simplifying 3x3 + 36x4 + -48x5 = 0 Solving 3x3 + 36x4 + -48x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(1 + 12x + -16x2) = 0 Ignore the factor 3.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 '(1 + 12x + -16x2)' equal to zero and attempt to solve: Simplifying 1 + 12x + -16x2 = 0 Solving 1 + 12x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.75x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.75x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.75x + x2 = 0 + 0.0625 -0.75x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.75x + x2 = 0.0625 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.0625 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.0625 + 0.140625 Combine like terms: 0.0625 + 0.140625 = 0.203125 0.140625 + -0.75x + x2 = 0.203125 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (x + -0.375) equal to 0.450693909 and -0.450693909.Subproblem 1
x + -0.375 = 0.450693909 Simplifying x + -0.375 = 0.450693909 Reorder the terms: -0.375 + x = 0.450693909 Solving -0.375 + x = 0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.450693909 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.450693909 + 0.375 x = 0.450693909 + 0.375 Combine like terms: 0.450693909 + 0.375 = 0.825693909 x = 0.825693909 Simplifying x = 0.825693909Subproblem 2
x + -0.375 = -0.450693909 Simplifying x + -0.375 = -0.450693909 Reorder the terms: -0.375 + x = -0.450693909 Solving -0.375 + x = -0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.450693909 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.450693909 + 0.375 x = -0.450693909 + 0.375 Combine like terms: -0.450693909 + 0.375 = -0.075693909 x = -0.075693909 Simplifying x = -0.075693909Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.825693909, -0.075693909}Solution
x = {0.825693909, -0.075693909}
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