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Simplifying 16x3 + -123x2 + 120x = 0 Reorder the terms: 120x + -123x2 + 16x3 = 0 Solving 120x + -123x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(120 + -123x + 16x2) = 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 + -123x + 16x2)' equal to zero and attempt to solve: Simplifying 120 + -123x + 16x2 = 0 Solving 120 + -123x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.5 + -7.6875x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7.6875x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7.6875x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7.6875x + x2 = 0 + -7.5 -7.6875x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7.6875x + x2 = -7.5 The x term is -7.6875x. Take half its coefficient (-3.84375). Square it (14.77441406) and add it to both sides. Add '14.77441406' to each side of the equation. -7.6875x + 14.77441406 + x2 = -7.5 + 14.77441406 Reorder the terms: 14.77441406 + -7.6875x + x2 = -7.5 + 14.77441406 Combine like terms: -7.5 + 14.77441406 = 7.27441406 14.77441406 + -7.6875x + x2 = 7.27441406 Factor a perfect square on the left side: (x + -3.84375)(x + -3.84375) = 7.27441406 Calculate the square root of the right side: 2.69711217 Break this problem into two subproblems by setting (x + -3.84375) equal to 2.69711217 and -2.69711217.Subproblem 1
x + -3.84375 = 2.69711217 Simplifying x + -3.84375 = 2.69711217 Reorder the terms: -3.84375 + x = 2.69711217 Solving -3.84375 + x = 2.69711217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.84375' to each side of the equation. -3.84375 + 3.84375 + x = 2.69711217 + 3.84375 Combine like terms: -3.84375 + 3.84375 = 0.00000 0.00000 + x = 2.69711217 + 3.84375 x = 2.69711217 + 3.84375 Combine like terms: 2.69711217 + 3.84375 = 6.54086217 x = 6.54086217 Simplifying x = 6.54086217Subproblem 2
x + -3.84375 = -2.69711217 Simplifying x + -3.84375 = -2.69711217 Reorder the terms: -3.84375 + x = -2.69711217 Solving -3.84375 + x = -2.69711217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.84375' to each side of the equation. -3.84375 + 3.84375 + x = -2.69711217 + 3.84375 Combine like terms: -3.84375 + 3.84375 = 0.00000 0.00000 + x = -2.69711217 + 3.84375 x = -2.69711217 + 3.84375 Combine like terms: -2.69711217 + 3.84375 = 1.14663783 x = 1.14663783 Simplifying x = 1.14663783Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.54086217, 1.14663783}Solution
x = {0, 6.54086217, 1.14663783}
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