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Simplifying x4 + -10x3 + -9x2 = 0 Reorder the terms: -9x2 + -10x3 + x4 = 0 Solving -9x2 + -10x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-9 + -10x + x2) = 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 '(-9 + -10x + x2)' equal to zero and attempt to solve: Simplifying -9 + -10x + x2 = 0 Solving -9 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -10x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -10x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10x + x2 = 0 + 9 -10x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -10x + x2 = 9 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 9 + 25 Reorder the terms: 25 + -10x + x2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + -10x + x2 = 34 Factor a perfect square on the left side: (x + -5)(x + -5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -5) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -5 = 5.830951895 Simplifying x + -5 = 5.830951895 Reorder the terms: -5 + x = 5.830951895 Solving -5 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.830951895 + 5 x = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 x = 10.830951895 Simplifying x = 10.830951895Subproblem 2
x + -5 = -5.830951895 Simplifying x + -5 = -5.830951895 Reorder the terms: -5 + x = -5.830951895 Solving -5 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.830951895 + 5 x = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 x = -0.830951895 Simplifying x = -0.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.830951895, -0.830951895}Solution
x = {0, 10.830951895, -0.830951895}
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