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Simplifying 12x3 + 35x2 + -48x = 0 Reorder the terms: -48x + 35x2 + 12x3 = 0 Solving -48x + 35x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-48 + 35x + 12x2) = 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 '(-48 + 35x + 12x2)' equal to zero and attempt to solve: Simplifying -48 + 35x + 12x2 = 0 Solving -48 + 35x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4 + 2.916666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.916666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.916666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.916666667x + x2 = 0 + 4 2.916666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.916666667x + x2 = 4 The x term is 2.916666667x. Take half its coefficient (1.458333334). Square it (2.126736113) and add it to both sides. Add '2.126736113' to each side of the equation. 2.916666667x + 2.126736113 + x2 = 4 + 2.126736113 Reorder the terms: 2.126736113 + 2.916666667x + x2 = 4 + 2.126736113 Combine like terms: 4 + 2.126736113 = 6.126736113 2.126736113 + 2.916666667x + x2 = 6.126736113 Factor a perfect square on the left side: (x + 1.458333334)(x + 1.458333334) = 6.126736113 Calculate the square root of the right side: 2.475224457 Break this problem into two subproblems by setting (x + 1.458333334) equal to 2.475224457 and -2.475224457.Subproblem 1
x + 1.458333334 = 2.475224457 Simplifying x + 1.458333334 = 2.475224457 Reorder the terms: 1.458333334 + x = 2.475224457 Solving 1.458333334 + x = 2.475224457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = 2.475224457 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = 2.475224457 + -1.458333334 x = 2.475224457 + -1.458333334 Combine like terms: 2.475224457 + -1.458333334 = 1.016891123 x = 1.016891123 Simplifying x = 1.016891123Subproblem 2
x + 1.458333334 = -2.475224457 Simplifying x + 1.458333334 = -2.475224457 Reorder the terms: 1.458333334 + x = -2.475224457 Solving 1.458333334 + x = -2.475224457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.458333334' to each side of the equation. 1.458333334 + -1.458333334 + x = -2.475224457 + -1.458333334 Combine like terms: 1.458333334 + -1.458333334 = 0.000000000 0.000000000 + x = -2.475224457 + -1.458333334 x = -2.475224457 + -1.458333334 Combine like terms: -2.475224457 + -1.458333334 = -3.933557791 x = -3.933557791 Simplifying x = -3.933557791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.016891123, -3.933557791}Solution
x = {0, 1.016891123, -3.933557791}
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