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Simplifying 2X4 + 5X3 + -5X2 = 0 Reorder the terms: -5X2 + 5X3 + 2X4 = 0 Solving -5X2 + 5X3 + 2X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X2'. X2(-5 + 5X + 2X2) = 0Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve: Simplifying X2 = 0 Solving X2 = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X2 = 0 Take the square root of each side: X = {0}Subproblem 2
Set the factor '(-5 + 5X + 2X2)' equal to zero and attempt to solve: Simplifying -5 + 5X + 2X2 = 0 Solving -5 + 5X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 2.5X + X2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.5X + 2.5 + X2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.5X + X2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.5X + X2 = 0 + 2.5 2.5X + X2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.5X + X2 = 2.5 The X term is 2.5X. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5X + 1.5625 + X2 = 2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5X + X2 = 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + 2.5X + X2 = 4.0625 Factor a perfect square on the left side: (X + 1.25)(X + 1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (X + 1.25) equal to 2.015564437 and -2.015564437.Subproblem 1
X + 1.25 = 2.015564437 Simplifying X + 1.25 = 2.015564437 Reorder the terms: 1.25 + X = 2.015564437 Solving 1.25 + X = 2.015564437 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = 2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 2.015564437 + -1.25 X = 2.015564437 + -1.25 Combine like terms: 2.015564437 + -1.25 = 0.765564437 X = 0.765564437 Simplifying X = 0.765564437Subproblem 2
X + 1.25 = -2.015564437 Simplifying X + 1.25 = -2.015564437 Reorder the terms: 1.25 + X = -2.015564437 Solving 1.25 + X = -2.015564437 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = -2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -2.015564437 + -1.25 X = -2.015564437 + -1.25 Combine like terms: -2.015564437 + -1.25 = -3.265564437 X = -3.265564437 Simplifying X = -3.265564437Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.765564437, -3.265564437}Solution
X = {0, 0.765564437, -3.265564437}
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