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Simplifying 3x4 + -3x3 + -2x2 = 0 Reorder the terms: -2x2 + -3x3 + 3x4 = 0 Solving -2x2 + -3x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-2 + -3x + 3x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-2 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + -3x + 3x2 = 0 Solving -2 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -1x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.6666666667 -1x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1x + x2 = 0.6666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.6666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 0.25 + -1x + x2 = 0.9166666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + -0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
x + -0.5 = 0.957427108 Simplifying x + -0.5 = 0.957427108 Reorder the terms: -0.5 + x = 0.957427108 Solving -0.5 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.957427108 + 0.5 x = 0.957427108 + 0.5 Combine like terms: 0.957427108 + 0.5 = 1.457427108 x = 1.457427108 Simplifying x = 1.457427108Subproblem 2
x + -0.5 = -0.957427108 Simplifying x + -0.5 = -0.957427108 Reorder the terms: -0.5 + x = -0.957427108 Solving -0.5 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.957427108 + 0.5 x = -0.957427108 + 0.5 Combine like terms: -0.957427108 + 0.5 = -0.457427108 x = -0.457427108 Simplifying x = -0.457427108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.457427108, -0.457427108}Solution
x = {0, 1.457427108, -0.457427108}
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