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Simplifying x = x2 + -12x + 27 Reorder the terms: x = 27 + -12x + x2 Solving x = 27 + -12x + x2 Solving for variable 'x'. Reorder the terms: -27 + x + 12x + -1x2 = 27 + -12x + x2 + -27 + 12x + -1x2 Combine like terms: x + 12x = 13x -27 + 13x + -1x2 = 27 + -12x + x2 + -27 + 12x + -1x2 Reorder the terms: -27 + 13x + -1x2 = 27 + -27 + -12x + 12x + x2 + -1x2 Combine like terms: 27 + -27 = 0 -27 + 13x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -27 + 13x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -27 + 13x + -1x2 = 0 + x2 + -1x2 -27 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -27 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -13x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -13x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -13x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -13x + x2 = 0 + -27 -13x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -13x + x2 = -27 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -27 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -27 + 42.25 Combine like terms: -27 + 42.25 = 15.25 42.25 + -13x + x2 = 15.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -6.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -6.5 = 3.905124838 Simplifying x + -6.5 = 3.905124838 Reorder the terms: -6.5 + x = 3.905124838 Solving -6.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.905124838 + 6.5 x = 3.905124838 + 6.5 Combine like terms: 3.905124838 + 6.5 = 10.405124838 x = 10.405124838 Simplifying x = 10.405124838Subproblem 2
x + -6.5 = -3.905124838 Simplifying x + -6.5 = -3.905124838 Reorder the terms: -6.5 + x = -3.905124838 Solving -6.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.905124838 + 6.5 x = -3.905124838 + 6.5 Combine like terms: -3.905124838 + 6.5 = 2.594875162 x = 2.594875162 Simplifying x = 2.594875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.405124838, 2.594875162}
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