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Simplifying 12x3 + -123x2 + 120x = 0 Reorder the terms: 120x + -123x2 + 12x3 = 0 Solving 120x + -123x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(40 + -41x + 4x2) = 0 Ignore the factor 3.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 '(40 + -41x + 4x2)' equal to zero and attempt to solve: Simplifying 40 + -41x + 4x2 = 0 Solving 40 + -41x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + -10.25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10.25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10.25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10.25x + x2 = 0 + -10 -10.25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10.25x + x2 = -10 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = -10 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -10 + 26.265625 Combine like terms: -10 + 26.265625 = 16.265625 26.265625 + -10.25x + x2 = 16.265625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 16.265625 Calculate the square root of the right side: 4.033066451 Break this problem into two subproblems by setting (x + -5.125) equal to 4.033066451 and -4.033066451.Subproblem 1
x + -5.125 = 4.033066451 Simplifying x + -5.125 = 4.033066451 Reorder the terms: -5.125 + x = 4.033066451 Solving -5.125 + x = 4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 4.033066451 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 4.033066451 + 5.125 x = 4.033066451 + 5.125 Combine like terms: 4.033066451 + 5.125 = 9.158066451 x = 9.158066451 Simplifying x = 9.158066451Subproblem 2
x + -5.125 = -4.033066451 Simplifying x + -5.125 = -4.033066451 Reorder the terms: -5.125 + x = -4.033066451 Solving -5.125 + x = -4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -4.033066451 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -4.033066451 + 5.125 x = -4.033066451 + 5.125 Combine like terms: -4.033066451 + 5.125 = 1.091933549 x = 1.091933549 Simplifying x = 1.091933549Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.158066451, 1.091933549}Solution
x = {0, 9.158066451, 1.091933549}
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