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Simplifying x2 + -8x = 9x + -12 Reorder the terms: -8x + x2 = 9x + -12 Reorder the terms: -8x + x2 = -12 + 9x Solving -8x + x2 = -12 + 9x Solving for variable 'x'. Reorder the terms: 12 + -8x + -9x + x2 = -12 + 9x + 12 + -9x Combine like terms: -8x + -9x = -17x 12 + -17x + x2 = -12 + 9x + 12 + -9x Reorder the terms: 12 + -17x + x2 = -12 + 12 + 9x + -9x Combine like terms: -12 + 12 = 0 12 + -17x + x2 = 0 + 9x + -9x 12 + -17x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 12 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -17x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -17x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -17x + x2 = 0 + -12 -17x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -17x + x2 = -12 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 = -12 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -12 + 72.25 Combine like terms: -12 + 72.25 = 60.25 72.25 + -17x + x2 = 60.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -8.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -8.5 = 7.762087348 Simplifying x + -8.5 = 7.762087348 Reorder the terms: -8.5 + x = 7.762087348 Solving -8.5 + x = 7.762087348 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 = 7.762087348 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.762087348 + 8.5 x = 7.762087348 + 8.5 Combine like terms: 7.762087348 + 8.5 = 16.262087348 x = 16.262087348 Simplifying x = 16.262087348Subproblem 2
x + -8.5 = -7.762087348 Simplifying x + -8.5 = -7.762087348 Reorder the terms: -8.5 + x = -7.762087348 Solving -8.5 + x = -7.762087348 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 = -7.762087348 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.762087348 + 8.5 x = -7.762087348 + 8.5 Combine like terms: -7.762087348 + 8.5 = 0.737912652 x = 0.737912652 Simplifying x = 0.737912652Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.262087348, 0.737912652}
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