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Simplifying -2x3 + 3x2 + 120x = 0 Reorder the terms: 120x + 3x2 + -2x3 = 0 Solving 120x + 3x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(120 + 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 '(120 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 120 + 3x + -2x2 = 0 Solving 120 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -60 + -1.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -1.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -1.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1.5x + x2 = 0 + 60 -1.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -1.5x + x2 = 60 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 = 60 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 60 + 0.5625 Combine like terms: 60 + 0.5625 = 60.5625 0.5625 + -1.5x + x2 = 60.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 60.5625 Calculate the square root of the right side: 7.782191208 Break this problem into two subproblems by setting (x + -0.75) equal to 7.782191208 and -7.782191208.Subproblem 1
x + -0.75 = 7.782191208 Simplifying x + -0.75 = 7.782191208 Reorder the terms: -0.75 + x = 7.782191208 Solving -0.75 + x = 7.782191208 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 = 7.782191208 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.782191208 + 0.75 x = 7.782191208 + 0.75 Combine like terms: 7.782191208 + 0.75 = 8.532191208 x = 8.532191208 Simplifying x = 8.532191208Subproblem 2
x + -0.75 = -7.782191208 Simplifying x + -0.75 = -7.782191208 Reorder the terms: -0.75 + x = -7.782191208 Solving -0.75 + x = -7.782191208 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 = -7.782191208 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.782191208 + 0.75 x = -7.782191208 + 0.75 Combine like terms: -7.782191208 + 0.75 = -7.032191208 x = -7.032191208 Simplifying x = -7.032191208Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.532191208, -7.032191208}Solution
x = {0, 8.532191208, -7.032191208}
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