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Simplifying 3x4 + -9x3 + -2x2 = 0 Reorder the terms: -2x2 + -9x3 + 3x4 = 0 Solving -2x2 + -9x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-2 + -9x + 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 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + -9x + 3x2 = 0 Solving -2 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -3x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -3x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -3x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.6666666667 -3x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -3x + x2 = 0.6666666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.6666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.6666666667 + 2.25 Combine like terms: 0.6666666667 + 2.25 = 2.9166666667 2.25 + -3x + x2 = 2.9166666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.9166666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + -1.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x + -1.5 = 1.707825128 Simplifying x + -1.5 = 1.707825128 Reorder the terms: -1.5 + x = 1.707825128 Solving -1.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.707825128 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.707825128 + 1.5 x = 1.707825128 + 1.5 Combine like terms: 1.707825128 + 1.5 = 3.207825128 x = 3.207825128 Simplifying x = 3.207825128Subproblem 2
x + -1.5 = -1.707825128 Simplifying x + -1.5 = -1.707825128 Reorder the terms: -1.5 + x = -1.707825128 Solving -1.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.707825128 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.707825128 + 1.5 x = -1.707825128 + 1.5 Combine like terms: -1.707825128 + 1.5 = -0.207825128 x = -0.207825128 Simplifying x = -0.207825128Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.207825128, -0.207825128}Solution
x = {0, 3.207825128, -0.207825128}
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