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Simplifying 3x3 + -19x2 = 6x Reorder the terms: -19x2 + 3x3 = 6x Solving -19x2 + 3x3 = 6x Solving for variable 'x'. Reorder the terms: -6x + -19x2 + 3x3 = 6x + -6x Combine like terms: 6x + -6x = 0 -6x + -19x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -19x + 3x2) = 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 '(-6 + -19x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -19x + 3x2 = 0 Solving -6 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.333333333x + x2 = 0 + 2 -6.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.333333333x + x2 = 2 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = 2 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 2 + 10.02777778 Combine like terms: 2 + 10.02777778 = 12.02777778 10.02777778 + -6.333333333x + x2 = 12.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 12.02777778 Calculate the square root of the right side: 3.468108675 Break this problem into two subproblems by setting (x + -3.166666667) equal to 3.468108675 and -3.468108675.Subproblem 1
x + -3.166666667 = 3.468108675 Simplifying x + -3.166666667 = 3.468108675 Reorder the terms: -3.166666667 + x = 3.468108675 Solving -3.166666667 + x = 3.468108675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 3.468108675 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 3.468108675 + 3.166666667 x = 3.468108675 + 3.166666667 Combine like terms: 3.468108675 + 3.166666667 = 6.634775342 x = 6.634775342 Simplifying x = 6.634775342Subproblem 2
x + -3.166666667 = -3.468108675 Simplifying x + -3.166666667 = -3.468108675 Reorder the terms: -3.166666667 + x = -3.468108675 Solving -3.166666667 + x = -3.468108675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -3.468108675 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -3.468108675 + 3.166666667 x = -3.468108675 + 3.166666667 Combine like terms: -3.468108675 + 3.166666667 = -0.301442008 x = -0.301442008 Simplifying x = -0.301442008Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.634775342, -0.301442008}Solution
x = {0, 6.634775342, -0.301442008}
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