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Simplifying 12x3 + -72x2 + 40x = 0 Reorder the terms: 40x + -72x2 + 12x3 = 0 Solving 40x + -72x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(10 + -18x + 3x2) = 0 Ignore the factor 4.Subproblem 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 '(10 + -18x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + -18x + 3x2 = 0 Solving 10 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -6x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -6x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + -3.333333333 -6x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -6x + x2 = -3.333333333 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 = -3.333333333 + 9 Reorder the terms: 9 + -6x + x2 = -3.333333333 + 9 Combine like terms: -3.333333333 + 9 = 5.666666667 9 + -6x + x2 = 5.666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x + -3) equal to 2.380476143 and -2.380476143.Subproblem 1
x + -3 = 2.380476143 Simplifying x + -3 = 2.380476143 Reorder the terms: -3 + x = 2.380476143 Solving -3 + x = 2.380476143 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 = 2.380476143 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.380476143 + 3 x = 2.380476143 + 3 Combine like terms: 2.380476143 + 3 = 5.380476143 x = 5.380476143 Simplifying x = 5.380476143Subproblem 2
x + -3 = -2.380476143 Simplifying x + -3 = -2.380476143 Reorder the terms: -3 + x = -2.380476143 Solving -3 + x = -2.380476143 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 = -2.380476143 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.380476143 + 3 x = -2.380476143 + 3 Combine like terms: -2.380476143 + 3 = 0.619523857 x = 0.619523857 Simplifying x = 0.619523857Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.380476143, 0.619523857}Solution
x = {0, 5.380476143, 0.619523857}
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