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Simplifying 5x4 + -45x3 + 10x2 = 0 Reorder the terms: 10x2 + -45x3 + 5x4 = 0 Solving 10x2 + -45x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(2 + -9x + x2) = 0 Ignore the factor 5.Subproblem 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 '(2 + -9x + x2)' equal to zero and attempt to solve: Simplifying 2 + -9x + x2 = 0 Solving 2 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -9x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -9x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9x + x2 = 0 + -2 -9x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -9x + x2 = -2 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -2 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + -9x + x2 = 18.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -4.5 = 4.272001873 Simplifying x + -4.5 = 4.272001873 Reorder the terms: -4.5 + x = 4.272001873 Solving -4.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.272001873 + 4.5 x = 4.272001873 + 4.5 Combine like terms: 4.272001873 + 4.5 = 8.772001873 x = 8.772001873 Simplifying x = 8.772001873Subproblem 2
x + -4.5 = -4.272001873 Simplifying x + -4.5 = -4.272001873 Reorder the terms: -4.5 + x = -4.272001873 Solving -4.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.272001873 + 4.5 x = -4.272001873 + 4.5 Combine like terms: -4.272001873 + 4.5 = 0.227998127 x = 0.227998127 Simplifying x = 0.227998127Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.772001873, 0.227998127}Solution
x = {0, 8.772001873, 0.227998127}
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