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Simplifying x3 + 28x2 + -11x = 0 Reorder the terms: -11x + 28x2 + x3 = 0 Solving -11x + 28x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 28x + 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 '(-11 + 28x + x2)' equal to zero and attempt to solve: Simplifying -11 + 28x + x2 = 0 Solving -11 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 28x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 28x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 28x + x2 = 0 + 11 28x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 28x + x2 = 11 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 11 + 196 Reorder the terms: 196 + 28x + x2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + 28x + x2 = 207 Factor a perfect square on the left side: (x + 14)(x + 14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (x + 14) equal to 14.38749457 and -14.38749457.Subproblem 1
x + 14 = 14.38749457 Simplifying x + 14 = 14.38749457 Reorder the terms: 14 + x = 14.38749457 Solving 14 + x = 14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.38749457 + -14 x = 14.38749457 + -14 Combine like terms: 14.38749457 + -14 = 0.38749457 x = 0.38749457 Simplifying x = 0.38749457Subproblem 2
x + 14 = -14.38749457 Simplifying x + 14 = -14.38749457 Reorder the terms: 14 + x = -14.38749457 Solving 14 + x = -14.38749457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.38749457 + -14 x = -14.38749457 + -14 Combine like terms: -14.38749457 + -14 = -28.38749457 x = -28.38749457 Simplifying x = -28.38749457Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38749457, -28.38749457}Solution
x = {0, 0.38749457, -28.38749457}
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