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Simplifying 3x5 + -18x4 + x3 = 0 Reorder the terms: x3 + -18x4 + 3x5 = 0 Solving x3 + -18x4 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(1 + -18x + 3x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(1 + -18x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -18x + 3x2 = 0 Solving 1 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -6x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -6x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -6x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + -0.3333333333 -6x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -6x + x2 = -0.3333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.3333333333 + 9 Reorder the terms: 9 + -6x + x2 = -0.3333333333 + 9 Combine like terms: -0.3333333333 + 9 = 8.6666666667 9 + -6x + x2 = 8.6666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.6666666667 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (x + -3) equal to 2.943920289 and -2.943920289.Subproblem 1
x + -3 = 2.943920289 Simplifying x + -3 = 2.943920289 Reorder the terms: -3 + x = 2.943920289 Solving -3 + x = 2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.943920289 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.943920289 + 3 x = 2.943920289 + 3 Combine like terms: 2.943920289 + 3 = 5.943920289 x = 5.943920289 Simplifying x = 5.943920289Subproblem 2
x + -3 = -2.943920289 Simplifying x + -3 = -2.943920289 Reorder the terms: -3 + x = -2.943920289 Solving -3 + x = -2.943920289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.943920289 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.943920289 + 3 x = -2.943920289 + 3 Combine like terms: -2.943920289 + 3 = 0.056079711 x = 0.056079711 Simplifying x = 0.056079711Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.943920289, 0.056079711}Solution
x = {5.943920289, 0.056079711}
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