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Simplifying 3x6 + -19x5 + -12x4 = 0 Reorder the terms: -12x4 + -19x5 + 3x6 = 0 Solving -12x4 + -19x5 + 3x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(-12 + -19x + 3x2) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-12 + -19x + 3x2)' equal to zero and attempt to solve: Simplifying -12 + -19x + 3x2 = 0 Solving -12 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6.333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.333333333x + x2 = 0 + 4 -6.333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.333333333x + x2 = 4 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 = 4 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 4 + 10.02777778 Combine like terms: 4 + 10.02777778 = 14.02777778 10.02777778 + -6.333333333x + x2 = 14.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 14.02777778 Calculate the square root of the right side: 3.745367509 Break this problem into two subproblems by setting (x + -3.166666667) equal to 3.745367509 and -3.745367509.Subproblem 1
x + -3.166666667 = 3.745367509 Simplifying x + -3.166666667 = 3.745367509 Reorder the terms: -3.166666667 + x = 3.745367509 Solving -3.166666667 + x = 3.745367509 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 = 3.745367509 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 3.745367509 + 3.166666667 x = 3.745367509 + 3.166666667 Combine like terms: 3.745367509 + 3.166666667 = 6.912034176 x = 6.912034176 Simplifying x = 6.912034176Subproblem 2
x + -3.166666667 = -3.745367509 Simplifying x + -3.166666667 = -3.745367509 Reorder the terms: -3.166666667 + x = -3.745367509 Solving -3.166666667 + x = -3.745367509 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 = -3.745367509 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -3.745367509 + 3.166666667 x = -3.745367509 + 3.166666667 Combine like terms: -3.745367509 + 3.166666667 = -0.578700842 x = -0.578700842 Simplifying x = -0.578700842Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.912034176, -0.578700842}Solution
x = {6.912034176, -0.578700842}
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