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Simplifying 5x3 + -6x2 + -120x = 0 Reorder the terms: -120x + -6x2 + 5x3 = 0 Solving -120x + -6x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-120 + -6x + 5x2) = 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 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -120 + -6x + 5x2 = 0 Solving -120 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24 + -1.2x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -1.2x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -1.2x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1.2x + x2 = 0 + 24 -1.2x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -1.2x + x2 = 24 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 24 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 24 + 0.36 Combine like terms: 24 + 0.36 = 24.36 0.36 + -1.2x + x2 = 24.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 24.36 Calculate the square root of the right side: 4.935585072 Break this problem into two subproblems by setting (x + -0.6) equal to 4.935585072 and -4.935585072.Subproblem 1
x + -0.6 = 4.935585072 Simplifying x + -0.6 = 4.935585072 Reorder the terms: -0.6 + x = 4.935585072 Solving -0.6 + x = 4.935585072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 4.935585072 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 4.935585072 + 0.6 x = 4.935585072 + 0.6 Combine like terms: 4.935585072 + 0.6 = 5.535585072 x = 5.535585072 Simplifying x = 5.535585072Subproblem 2
x + -0.6 = -4.935585072 Simplifying x + -0.6 = -4.935585072 Reorder the terms: -0.6 + x = -4.935585072 Solving -0.6 + x = -4.935585072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -4.935585072 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -4.935585072 + 0.6 x = -4.935585072 + 0.6 Combine like terms: -4.935585072 + 0.6 = -4.335585072 x = -4.335585072 Simplifying x = -4.335585072Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.535585072, -4.335585072}Solution
x = {0, 5.535585072, -4.335585072}
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