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Simplifying 121 = x2 + 6x Reorder the terms: 121 = 6x + x2 Solving 121 = 6x + x2 Solving for variable 'x'. Reorder the terms: 121 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 121 + -6x + -1x2 = 0 + x2 + -1x2 121 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 121 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -121 + 6x + x2 = 0 Move the constant term to the right: Add '121' to each side of the equation. -121 + 6x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 6x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 6x + x2 = 0 + 121 6x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 6x + x2 = 121 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 = 121 + 9 Reorder the terms: 9 + 6x + x2 = 121 + 9 Combine like terms: 121 + 9 = 130 9 + 6x + x2 = 130 Factor a perfect square on the left side: (x + 3)(x + 3) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 3) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 3 = 11.401754251 Simplifying x + 3 = 11.401754251 Reorder the terms: 3 + x = 11.401754251 Solving 3 + x = 11.401754251 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 = 11.401754251 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.401754251 + -3 x = 11.401754251 + -3 Combine like terms: 11.401754251 + -3 = 8.401754251 x = 8.401754251 Simplifying x = 8.401754251Subproblem 2
x + 3 = -11.401754251 Simplifying x + 3 = -11.401754251 Reorder the terms: 3 + x = -11.401754251 Solving 3 + x = -11.401754251 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 = -11.401754251 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.401754251 + -3 x = -11.401754251 + -3 Combine like terms: -11.401754251 + -3 = -14.401754251 x = -14.401754251 Simplifying x = -14.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.401754251, -14.401754251}
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