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Simplifying x2 + 6x = 124 Reorder the terms: 6x + x2 = 124 Solving 6x + x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 6x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 6x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 6x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 6x + x2 = 0 + 124 6x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 6x + x2 = 124 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 = 124 + 9 Reorder the terms: 9 + 6x + x2 = 124 + 9 Combine like terms: 124 + 9 = 133 9 + 6x + x2 = 133 Factor a perfect square on the left side: (x + 3)(x + 3) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + 3) equal to 11.532562595 and -11.532562595.Subproblem 1
x + 3 = 11.532562595 Simplifying x + 3 = 11.532562595 Reorder the terms: 3 + x = 11.532562595 Solving 3 + x = 11.532562595 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 = 11.532562595 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.532562595 + -3 x = 11.532562595 + -3 Combine like terms: 11.532562595 + -3 = 8.532562595 x = 8.532562595 Simplifying x = 8.532562595Subproblem 2
x + 3 = -11.532562595 Simplifying x + 3 = -11.532562595 Reorder the terms: 3 + x = -11.532562595 Solving 3 + x = -11.532562595 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 = -11.532562595 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.532562595 + -3 x = -11.532562595 + -3 Combine like terms: -11.532562595 + -3 = -14.532562595 x = -14.532562595 Simplifying x = -14.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.532562595, -14.532562595}
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