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Simplifying 16x3 + -4x2 + -11x = 0 Reorder the terms: -11x + -4x2 + 16x3 = 0 Solving -11x + -4x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + -4x + 16x2) = 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 '(-11 + -4x + 16x2)' equal to zero and attempt to solve: Simplifying -11 + -4x + 16x2 = 0 Solving -11 + -4x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.6875 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -0.25x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -0.25x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.6875 -0.25x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -0.25x + x2 = 0.6875 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 = 0.6875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.6875 + 0.015625 Combine like terms: 0.6875 + 0.015625 = 0.703125 0.015625 + -0.25x + x2 = 0.703125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.703125 Calculate the square root of the right side: 0.838525492 Break this problem into two subproblems by setting (x + -0.125) equal to 0.838525492 and -0.838525492.Subproblem 1
x + -0.125 = 0.838525492 Simplifying x + -0.125 = 0.838525492 Reorder the terms: -0.125 + x = 0.838525492 Solving -0.125 + x = 0.838525492 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 = 0.838525492 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.838525492 + 0.125 x = 0.838525492 + 0.125 Combine like terms: 0.838525492 + 0.125 = 0.963525492 x = 0.963525492 Simplifying x = 0.963525492Subproblem 2
x + -0.125 = -0.838525492 Simplifying x + -0.125 = -0.838525492 Reorder the terms: -0.125 + x = -0.838525492 Solving -0.125 + x = -0.838525492 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 = -0.838525492 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.838525492 + 0.125 x = -0.838525492 + 0.125 Combine like terms: -0.838525492 + 0.125 = -0.713525492 x = -0.713525492 Simplifying x = -0.713525492Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.963525492, -0.713525492}Solution
x = {0, 0.963525492, -0.713525492}
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