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Simplifying x3 + -17x2 = -17x Reorder the terms: -17x2 + x3 = -17x Solving -17x2 + x3 = -17x Solving for variable 'x'. Reorder the terms: 17x + -17x2 + x3 = -17x + 17x Combine like terms: -17x + 17x = 0 17x + -17x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(17 + -17x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(17 + -17x + x2)' equal to zero and attempt to solve: Simplifying 17 + -17x + x2 = 0 Solving 17 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -17x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -17x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -17x + x2 = 0 + -17 -17x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -17x + x2 = -17 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 = -17 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -17 + 72.25 Combine like terms: -17 + 72.25 = 55.25 72.25 + -17x + x2 = 55.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -8.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -8.5 = 7.433034374 Simplifying x + -8.5 = 7.433034374 Reorder the terms: -8.5 + x = 7.433034374 Solving -8.5 + x = 7.433034374 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 = 7.433034374 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.433034374 + 8.5 x = 7.433034374 + 8.5 Combine like terms: 7.433034374 + 8.5 = 15.933034374 x = 15.933034374 Simplifying x = 15.933034374Subproblem 2
x + -8.5 = -7.433034374 Simplifying x + -8.5 = -7.433034374 Reorder the terms: -8.5 + x = -7.433034374 Solving -8.5 + x = -7.433034374 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 = -7.433034374 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.433034374 + 8.5 x = -7.433034374 + 8.5 Combine like terms: -7.433034374 + 8.5 = 1.066965626 x = 1.066965626 Simplifying x = 1.066965626Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.933034374, 1.066965626}Solution
x = {0, 15.933034374, 1.066965626}
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