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Simplifying x2 + -17x + -408 = 0 Reorder the terms: -408 + -17x + x2 = 0 Solving -408 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '408' to each side of the equation. -408 + -17x + 408 + x2 = 0 + 408 Reorder the terms: -408 + 408 + -17x + x2 = 0 + 408 Combine like terms: -408 + 408 = 0 0 + -17x + x2 = 0 + 408 -17x + x2 = 0 + 408 Combine like terms: 0 + 408 = 408 -17x + x2 = 408 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 = 408 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 408 + 72.25 Combine like terms: 408 + 72.25 = 480.25 72.25 + -17x + x2 = 480.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (x + -8.5) equal to 21.914607001 and -21.914607001.Subproblem 1
x + -8.5 = 21.914607001 Simplifying x + -8.5 = 21.914607001 Reorder the terms: -8.5 + x = 21.914607001 Solving -8.5 + x = 21.914607001 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 = 21.914607001 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 21.914607001 + 8.5 x = 21.914607001 + 8.5 Combine like terms: 21.914607001 + 8.5 = 30.414607001 x = 30.414607001 Simplifying x = 30.414607001Subproblem 2
x + -8.5 = -21.914607001 Simplifying x + -8.5 = -21.914607001 Reorder the terms: -8.5 + x = -21.914607001 Solving -8.5 + x = -21.914607001 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 = -21.914607001 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -21.914607001 + 8.5 x = -21.914607001 + 8.5 Combine like terms: -21.914607001 + 8.5 = -13.414607001 x = -13.414607001 Simplifying x = -13.414607001Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.414607001, -13.414607001}
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