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Simplifying x2 + 6x = 108 Reorder the terms: 6x + x2 = 108 Solving 6x + x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + 6x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 6x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 6x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 6x + x2 = 0 + 108 6x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 6x + x2 = 108 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 = 108 + 9 Reorder the terms: 9 + 6x + x2 = 108 + 9 Combine like terms: 108 + 9 = 117 9 + 6x + x2 = 117 Factor a perfect square on the left side: (x + 3)(x + 3) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 3) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 3 = 10.816653826 Simplifying x + 3 = 10.816653826 Reorder the terms: 3 + x = 10.816653826 Solving 3 + x = 10.816653826 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 = 10.816653826 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.816653826 + -3 x = 10.816653826 + -3 Combine like terms: 10.816653826 + -3 = 7.816653826 x = 7.816653826 Simplifying x = 7.816653826Subproblem 2
x + 3 = -10.816653826 Simplifying x + 3 = -10.816653826 Reorder the terms: 3 + x = -10.816653826 Solving 3 + x = -10.816653826 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 = -10.816653826 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.816653826 + -3 x = -10.816653826 + -3 Combine like terms: -10.816653826 + -3 = -13.816653826 x = -13.816653826 Simplifying x = -13.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.816653826, -13.816653826}
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