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Simplifying 2x4 + -9x3 + -4x2 = 0 Reorder the terms: -4x2 + -9x3 + 2x4 = 0 Solving -4x2 + -9x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -9x + 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 '(-4 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + -9x + 2x2 = 0 Solving -4 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -4.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.5x + x2 = 0 + 2 -4.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.5x + x2 = 2 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 2 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 2 + 5.0625 Combine like terms: 2 + 5.0625 = 7.0625 5.0625 + -4.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -2.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -2.25 = 2.657536453 Simplifying x + -2.25 = 2.657536453 Reorder the terms: -2.25 + x = 2.657536453 Solving -2.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.657536453 + 2.25 x = 2.657536453 + 2.25 Combine like terms: 2.657536453 + 2.25 = 4.907536453 x = 4.907536453 Simplifying x = 4.907536453Subproblem 2
x + -2.25 = -2.657536453 Simplifying x + -2.25 = -2.657536453 Reorder the terms: -2.25 + x = -2.657536453 Solving -2.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.657536453 + 2.25 x = -2.657536453 + 2.25 Combine like terms: -2.657536453 + 2.25 = -0.407536453 x = -0.407536453 Simplifying x = -0.407536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.907536453, -0.407536453}Solution
x = {0, 4.907536453, -0.407536453}
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