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Simplifying x(x + 6) = 122 Reorder the terms: x(6 + x) = 122 (6 * x + x * x) = 122 (6x + x2) = 122 Solving 6x + x2 = 122 Solving for variable 'x'. Reorder the terms: -122 + 6x + x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -122 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + 6x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + 6x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 6x + x2 = 0 + 122 6x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 6x + x2 = 122 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 = 122 + 9 Reorder the terms: 9 + 6x + x2 = 122 + 9 Combine like terms: 122 + 9 = 131 9 + 6x + x2 = 131 Factor a perfect square on the left side: (x + 3)(x + 3) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + 3) equal to 11.445523142 and -11.445523142.Subproblem 1
x + 3 = 11.445523142 Simplifying x + 3 = 11.445523142 Reorder the terms: 3 + x = 11.445523142 Solving 3 + x = 11.445523142 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 = 11.445523142 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.445523142 + -3 x = 11.445523142 + -3 Combine like terms: 11.445523142 + -3 = 8.445523142 x = 8.445523142 Simplifying x = 8.445523142Subproblem 2
x + 3 = -11.445523142 Simplifying x + 3 = -11.445523142 Reorder the terms: 3 + x = -11.445523142 Solving 3 + x = -11.445523142 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 = -11.445523142 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.445523142 + -3 x = -11.445523142 + -3 Combine like terms: -11.445523142 + -3 = -14.445523142 x = -14.445523142 Simplifying x = -14.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.445523142, -14.445523142}
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