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Simplifying x3 + -96x2 + 576x = 0 Reorder the terms: 576x + -96x2 + x3 = 0 Solving 576x + -96x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(576 + -96x + x2) = 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 '(576 + -96x + x2)' equal to zero and attempt to solve: Simplifying 576 + -96x + x2 = 0 Solving 576 + -96x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-576' to each side of the equation. 576 + -96x + -576 + x2 = 0 + -576 Reorder the terms: 576 + -576 + -96x + x2 = 0 + -576 Combine like terms: 576 + -576 = 0 0 + -96x + x2 = 0 + -576 -96x + x2 = 0 + -576 Combine like terms: 0 + -576 = -576 -96x + x2 = -576 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = -576 + 2304 Reorder the terms: 2304 + -96x + x2 = -576 + 2304 Combine like terms: -576 + 2304 = 1728 2304 + -96x + x2 = 1728 Factor a perfect square on the left side: (x + -48)(x + -48) = 1728 Calculate the square root of the right side: 41.569219382 Break this problem into two subproblems by setting (x + -48) equal to 41.569219382 and -41.569219382.Subproblem 1
x + -48 = 41.569219382 Simplifying x + -48 = 41.569219382 Reorder the terms: -48 + x = 41.569219382 Solving -48 + x = 41.569219382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 41.569219382 + 48 Combine like terms: -48 + 48 = 0 0 + x = 41.569219382 + 48 x = 41.569219382 + 48 Combine like terms: 41.569219382 + 48 = 89.569219382 x = 89.569219382 Simplifying x = 89.569219382Subproblem 2
x + -48 = -41.569219382 Simplifying x + -48 = -41.569219382 Reorder the terms: -48 + x = -41.569219382 Solving -48 + x = -41.569219382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -41.569219382 + 48 Combine like terms: -48 + 48 = 0 0 + x = -41.569219382 + 48 x = -41.569219382 + 48 Combine like terms: -41.569219382 + 48 = 6.430780618 x = 6.430780618 Simplifying x = 6.430780618Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.569219382, 6.430780618}Solution
x = {0, 89.569219382, 6.430780618}
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