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Simplifying 0 = x2 + -6x + -38 Reorder the terms: 0 = -38 + -6x + x2 Solving 0 = -38 + -6x + x2 Solving for variable 'x'. Combine like terms: 0 + 38 = 38 38 + 6x + -1x2 = -38 + -6x + x2 + 38 + 6x + -1x2 Reorder the terms: 38 + 6x + -1x2 = -38 + 38 + -6x + 6x + x2 + -1x2 Combine like terms: -38 + 38 = 0 38 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2 38 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 38 + 6x + -1x2 = 0 + x2 + -1x2 38 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -38 + -6x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + -6x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -6x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -6x + x2 = 0 + 38 -6x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -6x + x2 = 38 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 38 + 9 Reorder the terms: 9 + -6x + x2 = 38 + 9 Combine like terms: 38 + 9 = 47 9 + -6x + x2 = 47 Factor a perfect square on the left side: (x + -3)(x + -3) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -3) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -3 = 6.8556546 Simplifying x + -3 = 6.8556546 Reorder the terms: -3 + x = 6.8556546 Solving -3 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.8556546 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.8556546 + 3 x = 6.8556546 + 3 Combine like terms: 6.8556546 + 3 = 9.8556546 x = 9.8556546 Simplifying x = 9.8556546Subproblem 2
x + -3 = -6.8556546 Simplifying x + -3 = -6.8556546 Reorder the terms: -3 + x = -6.8556546 Solving -3 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.8556546 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.8556546 + 3 x = -6.8556546 + 3 Combine like terms: -6.8556546 + 3 = -3.8556546 x = -3.8556546 Simplifying x = -3.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.8556546, -3.8556546}
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