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Simplifying 8x3 + -12x2 + -6x = 0 Reorder the terms: -6x + -12x2 + 8x3 = 0 Solving -6x + -12x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + -6x + 4x2) = 0 Ignore the factor 2.Subproblem 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 '(-3 + -6x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + -6x + 4x2 = 0 Solving -3 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.5x + x2 = 0 + 0.75 -1.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.5x + x2 = 0.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.75 + 0.5625 Combine like terms: 0.75 + 0.5625 = 1.3125 0.5625 + -1.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -0.75) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -0.75 = 1.145643924 Simplifying x + -0.75 = 1.145643924 Reorder the terms: -0.75 + x = 1.145643924 Solving -0.75 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.145643924 + 0.75 x = 1.145643924 + 0.75 Combine like terms: 1.145643924 + 0.75 = 1.895643924 x = 1.895643924 Simplifying x = 1.895643924Subproblem 2
x + -0.75 = -1.145643924 Simplifying x + -0.75 = -1.145643924 Reorder the terms: -0.75 + x = -1.145643924 Solving -0.75 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.145643924 + 0.75 x = -1.145643924 + 0.75 Combine like terms: -1.145643924 + 0.75 = -0.395643924 x = -0.395643924 Simplifying x = -0.395643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.895643924, -0.395643924}Solution
x = {0, 1.895643924, -0.395643924}
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