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Simplifying 8x3 + -5x2 + -1x = 0 Reorder the terms: -1x + -5x2 + 8x3 = 0 Solving -1x + -5x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + -5x + 8x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = 0.22265625 0.09765625 + -0.625x + x2 = 0.22265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
x + -0.3125 = 0.471864652 Simplifying x + -0.3125 = 0.471864652 Reorder the terms: -0.3125 + x = 0.471864652 Solving -0.3125 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.471864652 + 0.3125 x = 0.471864652 + 0.3125 Combine like terms: 0.471864652 + 0.3125 = 0.784364652 x = 0.784364652 Simplifying x = 0.784364652Subproblem 2
x + -0.3125 = -0.471864652 Simplifying x + -0.3125 = -0.471864652 Reorder the terms: -0.3125 + x = -0.471864652 Solving -0.3125 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.471864652 + 0.3125 x = -0.471864652 + 0.3125 Combine like terms: -0.471864652 + 0.3125 = -0.159364652 x = -0.159364652 Simplifying x = -0.159364652Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.784364652, -0.159364652}Solution
x = {0, 0.784364652, -0.159364652}
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