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Simplifying 8X3 + X2 + -50X = 0 Reorder the terms: -50X + X2 + 8X3 = 0 Solving -50X + X2 + 8X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-50 + X + 8X2) = 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 '(-50 + X + 8X2)' equal to zero and attempt to solve: Simplifying -50 + X + 8X2 = 0 Solving -50 + X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.25 + 0.125X + X2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.125X + 6.25 + X2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.125X + X2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.125X + X2 = 0 + 6.25 0.125X + X2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.125X + X2 = 6.25 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125X + 0.25 + X2 = 6.25 + 0.25 Reorder the terms: 0.25 + 0.125X + X2 = 6.25 + 0.25 Combine like terms: 6.25 + 0.25 = 6.5 0.25 + 0.125X + X2 = 6.5 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (X + 0.5) equal to 2.549509757 and -2.549509757.Subproblem 1
X + 0.5 = 2.549509757 Simplifying X + 0.5 = 2.549509757 Reorder the terms: 0.5 + X = 2.549509757 Solving 0.5 + X = 2.549509757 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 2.549509757 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 2.549509757 + -0.5 X = 2.549509757 + -0.5 Combine like terms: 2.549509757 + -0.5 = 2.049509757 X = 2.049509757 Simplifying X = 2.049509757Subproblem 2
X + 0.5 = -2.549509757 Simplifying X + 0.5 = -2.549509757 Reorder the terms: 0.5 + X = -2.549509757 Solving 0.5 + X = -2.549509757 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -2.549509757 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -2.549509757 + -0.5 X = -2.549509757 + -0.5 Combine like terms: -2.549509757 + -0.5 = -3.049509757 X = -3.049509757 Simplifying X = -3.049509757Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.049509757, -3.049509757}Solution
X = {0, 2.049509757, -3.049509757}
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