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Simplifying x + 4 = x2 + -12x + 38 Reorder the terms: 4 + x = x2 + -12x + 38 Reorder the terms: 4 + x = 38 + -12x + x2 Solving 4 + x = 38 + -12x + x2 Solving for variable 'x'. Reorder the terms: 4 + -38 + x + 12x + -1x2 = 38 + -12x + x2 + -38 + 12x + -1x2 Combine like terms: 4 + -38 = -34 -34 + x + 12x + -1x2 = 38 + -12x + x2 + -38 + 12x + -1x2 Combine like terms: x + 12x = 13x -34 + 13x + -1x2 = 38 + -12x + x2 + -38 + 12x + -1x2 Reorder the terms: -34 + 13x + -1x2 = 38 + -38 + -12x + 12x + x2 + -1x2 Combine like terms: 38 + -38 = 0 -34 + 13x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -34 + 13x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -34 + 13x + -1x2 = 0 + x2 + -1x2 -34 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -34 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 34 + -13x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -13x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -13x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -13x + x2 = 0 + -34 -13x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -13x + x2 = -34 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 = -34 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -34 + 42.25 Combine like terms: -34 + 42.25 = 8.25 42.25 + -13x + x2 = 8.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -6.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -6.5 = 2.872281323 Simplifying x + -6.5 = 2.872281323 Reorder the terms: -6.5 + x = 2.872281323 Solving -6.5 + x = 2.872281323 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 = 2.872281323 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 2.872281323 + 6.5 x = 2.872281323 + 6.5 Combine like terms: 2.872281323 + 6.5 = 9.372281323 x = 9.372281323 Simplifying x = 9.372281323Subproblem 2
x + -6.5 = -2.872281323 Simplifying x + -6.5 = -2.872281323 Reorder the terms: -6.5 + x = -2.872281323 Solving -6.5 + x = -2.872281323 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 = -2.872281323 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -2.872281323 + 6.5 x = -2.872281323 + 6.5 Combine like terms: -2.872281323 + 6.5 = 3.627718677 x = 3.627718677 Simplifying x = 3.627718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.372281323, 3.627718677}
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