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Simplifying x4 + 17x3 + -8x2 = 0 Reorder the terms: -8x2 + 17x3 + x4 = 0 Solving -8x2 + 17x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-8 + 17x + 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 '(-8 + 17x + x2)' equal to zero and attempt to solve: Simplifying -8 + 17x + x2 = 0 Solving -8 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 17x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 17x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 17x + x2 = 0 + 8 17x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 17x + x2 = 8 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 8 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 8 + 72.25 Combine like terms: 8 + 72.25 = 80.25 72.25 + 17x + x2 = 80.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 8.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 8.5 = 8.958236434 Simplifying x + 8.5 = 8.958236434 Reorder the terms: 8.5 + x = 8.958236434 Solving 8.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.958236434 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.958236434 + -8.5 x = 8.958236434 + -8.5 Combine like terms: 8.958236434 + -8.5 = 0.458236434 x = 0.458236434 Simplifying x = 0.458236434Subproblem 2
x + 8.5 = -8.958236434 Simplifying x + 8.5 = -8.958236434 Reorder the terms: 8.5 + x = -8.958236434 Solving 8.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.958236434 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.958236434 + -8.5 x = -8.958236434 + -8.5 Combine like terms: -8.958236434 + -8.5 = -17.458236434 x = -17.458236434 Simplifying x = -17.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.458236434, -17.458236434}Solution
x = {0, 0.458236434, -17.458236434}
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