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Simplifying X3 + 7X2 + -13X = 0 Reorder the terms: -13X + 7X2 + X3 = 0 Solving -13X + 7X2 + X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-13 + 7X + 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 '(-13 + 7X + X2)' equal to zero and attempt to solve: Simplifying -13 + 7X + X2 = 0 Solving -13 + 7X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 7X + 13 + X2 = 0 + 13 Reorder the terms: -13 + 13 + 7X + X2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 7X + X2 = 0 + 13 7X + X2 = 0 + 13 Combine like terms: 0 + 13 = 13 7X + X2 = 13 The X term is 7X. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7X + 12.25 + X2 = 13 + 12.25 Reorder the terms: 12.25 + 7X + X2 = 13 + 12.25 Combine like terms: 13 + 12.25 = 25.25 12.25 + 7X + X2 = 25.25 Factor a perfect square on the left side: (X + 3.5)(X + 3.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (X + 3.5) equal to 5.024937811 and -5.024937811.Subproblem 1
X + 3.5 = 5.024937811 Simplifying X + 3.5 = 5.024937811 Reorder the terms: 3.5 + X = 5.024937811 Solving 3.5 + X = 5.024937811 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = 5.024937811 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = 5.024937811 + -3.5 X = 5.024937811 + -3.5 Combine like terms: 5.024937811 + -3.5 = 1.524937811 X = 1.524937811 Simplifying X = 1.524937811Subproblem 2
X + 3.5 = -5.024937811 Simplifying X + 3.5 = -5.024937811 Reorder the terms: 3.5 + X = -5.024937811 Solving 3.5 + X = -5.024937811 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = -5.024937811 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = -5.024937811 + -3.5 X = -5.024937811 + -3.5 Combine like terms: -5.024937811 + -3.5 = -8.524937811 X = -8.524937811 Simplifying X = -8.524937811Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.524937811, -8.524937811}Solution
X = {0, 1.524937811, -8.524937811}
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