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Simplifying 3x3 + 19x2 + -6x = 0 Reorder the terms: -6x + 19x2 + 3x3 = 0 Solving -6x + 19x2 + 3x3 = 0 Solving for variable 'x'. 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 = 0.301442008 x = 0.301442008 Simplifying x = 0.301442008Subproblem 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 = -6.634775342 x = -6.634775342 Simplifying x = -6.634775342Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.301442008, -6.634775342}Solution
x = {0, 0.301442008, -6.634775342}
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