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Simplifying -80x5 + 20x4 + 15x3 = 0 Reorder the terms: 15x3 + 20x4 + -80x5 = 0 Solving 15x3 + 20x4 + -80x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x3'. 5x3(3 + 4x + -16x2) = 0 Ignore the factor 5.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 '(3 + 4x + -16x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + -16x2 = 0 Solving 3 + 4x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.25x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.25x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.1875 -0.25x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.25x + x2 = 0.1875 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.1875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.1875 + 0.015625 Combine like terms: 0.1875 + 0.015625 = 0.203125 0.015625 + -0.25x + x2 = 0.203125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (x + -0.125) equal to 0.450693909 and -0.450693909.Subproblem 1
x + -0.125 = 0.450693909 Simplifying x + -0.125 = 0.450693909 Reorder the terms: -0.125 + x = 0.450693909 Solving -0.125 + x = 0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.450693909 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.450693909 + 0.125 x = 0.450693909 + 0.125 Combine like terms: 0.450693909 + 0.125 = 0.575693909 x = 0.575693909 Simplifying x = 0.575693909Subproblem 2
x + -0.125 = -0.450693909 Simplifying x + -0.125 = -0.450693909 Reorder the terms: -0.125 + x = -0.450693909 Solving -0.125 + x = -0.450693909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.450693909 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.450693909 + 0.125 x = -0.450693909 + 0.125 Combine like terms: -0.450693909 + 0.125 = -0.325693909 x = -0.325693909 Simplifying x = -0.325693909Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.575693909, -0.325693909}Solution
x = {0.575693909, -0.325693909}
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