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Simplifying 2x3 + -28x2 + -48x = 0 Reorder the terms: -48x + -28x2 + 2x3 = 0 Solving -48x + -28x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-24 + -14x + x2) = 0 Ignore the factor 2.Subproblem 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 '(-24 + -14x + x2)' equal to zero and attempt to solve: Simplifying -24 + -14x + x2 = 0 Solving -24 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -14x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -14x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -14x + x2 = 0 + 24 -14x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -14x + x2 = 24 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 24 + 49 Reorder the terms: 49 + -14x + x2 = 24 + 49 Combine like terms: 24 + 49 = 73 49 + -14x + x2 = 73 Factor a perfect square on the left side: (x + -7)(x + -7) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -7) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -7 = 8.544003745 Simplifying x + -7 = 8.544003745 Reorder the terms: -7 + x = 8.544003745 Solving -7 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.544003745 + 7 x = 8.544003745 + 7 Combine like terms: 8.544003745 + 7 = 15.544003745 x = 15.544003745 Simplifying x = 15.544003745Subproblem 2
x + -7 = -8.544003745 Simplifying x + -7 = -8.544003745 Reorder the terms: -7 + x = -8.544003745 Solving -7 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.544003745 + 7 x = -8.544003745 + 7 Combine like terms: -8.544003745 + 7 = -1.544003745 x = -1.544003745 Simplifying x = -1.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.544003745, -1.544003745}Solution
x = {0, 15.544003745, -1.544003745}
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