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Simplifying 12x3 + -4x2 + -18x = 0 Reorder the terms: -18x + -4x2 + 12x3 = 0 Solving -18x + -4x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + -2x + 6x2) = 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 '(-9 + -2x + 6x2)' equal to zero and attempt to solve: Simplifying -9 + -2x + 6x2 = 0 Solving -9 + -2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.3333333333x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.3333333333x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.3333333333x + x2 = 0 + 1.5 -0.3333333333x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.3333333333x + x2 = 1.5 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 1.5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 1.5 + 0.02777777779 Combine like terms: 1.5 + 0.02777777779 = 1.52777777779 0.02777777779 + -0.3333333333x + x2 = 1.52777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 1.52777777779 Calculate the square root of the right side: 1.236033081 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.236033081 and -1.236033081.Subproblem 1
x + -0.1666666667 = 1.236033081 Simplifying x + -0.1666666667 = 1.236033081 Reorder the terms: -0.1666666667 + x = 1.236033081 Solving -0.1666666667 + x = 1.236033081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.236033081 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.236033081 + 0.1666666667 x = 1.236033081 + 0.1666666667 Combine like terms: 1.236033081 + 0.1666666667 = 1.4026997477 x = 1.4026997477 Simplifying x = 1.4026997477Subproblem 2
x + -0.1666666667 = -1.236033081 Simplifying x + -0.1666666667 = -1.236033081 Reorder the terms: -0.1666666667 + x = -1.236033081 Solving -0.1666666667 + x = -1.236033081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.236033081 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.236033081 + 0.1666666667 x = -1.236033081 + 0.1666666667 Combine like terms: -1.236033081 + 0.1666666667 = -1.0693664143 x = -1.0693664143 Simplifying x = -1.0693664143Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4026997477, -1.0693664143}Solution
x = {0, 1.4026997477, -1.0693664143}
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