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Simplifying x2 + 6x + -38 = 0 Reorder the terms: -38 + 6x + x2 = 0 Solving -38 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. 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 = 3.8556546 x = 3.8556546 Simplifying x = 3.8556546Subproblem 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 = -9.8556546 x = -9.8556546 Simplifying x = -9.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8556546, -9.8556546}
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