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Simplifying 2x3 + 3x2 + -336x = 0 Reorder the terms: -336x + 3x2 + 2x3 = 0 Solving -336x + 3x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-336 + 3x + 2x2) = 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 '(-336 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -336 + 3x + 2x2 = 0 Solving -336 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -168 + 1.5x + x2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + 1.5x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 1.5x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 1.5x + x2 = 0 + 168 1.5x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 1.5x + x2 = 168 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 168 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 168 + 0.5625 Combine like terms: 168 + 0.5625 = 168.5625 0.5625 + 1.5x + x2 = 168.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 168.5625 Calculate the square root of the right side: 12.983162173 Break this problem into two subproblems by setting (x + 0.75) equal to 12.983162173 and -12.983162173.Subproblem 1
x + 0.75 = 12.983162173 Simplifying x + 0.75 = 12.983162173 Reorder the terms: 0.75 + x = 12.983162173 Solving 0.75 + x = 12.983162173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 12.983162173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 12.983162173 + -0.75 x = 12.983162173 + -0.75 Combine like terms: 12.983162173 + -0.75 = 12.233162173 x = 12.233162173 Simplifying x = 12.233162173Subproblem 2
x + 0.75 = -12.983162173 Simplifying x + 0.75 = -12.983162173 Reorder the terms: 0.75 + x = -12.983162173 Solving 0.75 + x = -12.983162173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -12.983162173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -12.983162173 + -0.75 x = -12.983162173 + -0.75 Combine like terms: -12.983162173 + -0.75 = -13.733162173 x = -13.733162173 Simplifying x = -13.733162173Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.233162173, -13.733162173}Solution
x = {0, 12.233162173, -13.733162173}
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