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Simplifying 3x3 + -2x2 + -72x = 0 Reorder the terms: -72x + -2x2 + 3x3 = 0 Solving -72x + -2x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-72 + -2x + 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 '(-72 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -72 + -2x + 3x2 = 0 Solving -72 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -0.6666666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -0.6666666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -0.6666666667x + x2 = 0 + 24 -0.6666666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -0.6666666667x + x2 = 24 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 24 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 24 + 0.1111111112 Combine like terms: 24 + 0.1111111112 = 24.1111111112 0.1111111112 + -0.6666666667x + x2 = 24.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 24.1111111112 Calculate the square root of the right side: 4.910306621 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 4.910306621 and -4.910306621.Subproblem 1
x + -0.3333333334 = 4.910306621 Simplifying x + -0.3333333334 = 4.910306621 Reorder the terms: -0.3333333334 + x = 4.910306621 Solving -0.3333333334 + x = 4.910306621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 4.910306621 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 4.910306621 + 0.3333333334 x = 4.910306621 + 0.3333333334 Combine like terms: 4.910306621 + 0.3333333334 = 5.2436399544 x = 5.2436399544 Simplifying x = 5.2436399544Subproblem 2
x + -0.3333333334 = -4.910306621 Simplifying x + -0.3333333334 = -4.910306621 Reorder the terms: -0.3333333334 + x = -4.910306621 Solving -0.3333333334 + x = -4.910306621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -4.910306621 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -4.910306621 + 0.3333333334 x = -4.910306621 + 0.3333333334 Combine like terms: -4.910306621 + 0.3333333334 = -4.5769732876 x = -4.5769732876 Simplifying x = -4.5769732876Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2436399544, -4.5769732876}Solution
x = {0, 5.2436399544, -4.5769732876}
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