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Simplifying 4x3 + 120x2 + -819x = 0 Reorder the terms: -819x + 120x2 + 4x3 = 0 Solving -819x + 120x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-819 + 120x + 4x2) = 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 '(-819 + 120x + 4x2)' equal to zero and attempt to solve: Simplifying -819 + 120x + 4x2 = 0 Solving -819 + 120x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -204.75 + 30x + x2 = 0 Move the constant term to the right: Add '204.75' to each side of the equation. -204.75 + 30x + 204.75 + x2 = 0 + 204.75 Reorder the terms: -204.75 + 204.75 + 30x + x2 = 0 + 204.75 Combine like terms: -204.75 + 204.75 = 0.00 0.00 + 30x + x2 = 0 + 204.75 30x + x2 = 0 + 204.75 Combine like terms: 0 + 204.75 = 204.75 30x + x2 = 204.75 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 204.75 + 225 Reorder the terms: 225 + 30x + x2 = 204.75 + 225 Combine like terms: 204.75 + 225 = 429.75 225 + 30x + x2 = 429.75 Factor a perfect square on the left side: (x + 15)(x + 15) = 429.75 Calculate the square root of the right side: 20.730412442 Break this problem into two subproblems by setting (x + 15) equal to 20.730412442 and -20.730412442.Subproblem 1
x + 15 = 20.730412442 Simplifying x + 15 = 20.730412442 Reorder the terms: 15 + x = 20.730412442 Solving 15 + x = 20.730412442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 20.730412442 + -15 Combine like terms: 15 + -15 = 0 0 + x = 20.730412442 + -15 x = 20.730412442 + -15 Combine like terms: 20.730412442 + -15 = 5.730412442 x = 5.730412442 Simplifying x = 5.730412442Subproblem 2
x + 15 = -20.730412442 Simplifying x + 15 = -20.730412442 Reorder the terms: 15 + x = -20.730412442 Solving 15 + x = -20.730412442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -20.730412442 + -15 Combine like terms: 15 + -15 = 0 0 + x = -20.730412442 + -15 x = -20.730412442 + -15 Combine like terms: -20.730412442 + -15 = -35.730412442 x = -35.730412442 Simplifying x = -35.730412442Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.730412442, -35.730412442}Solution
x = {0, 5.730412442, -35.730412442}
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