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Simplifying x2 + 12x + 121 = 225 Reorder the terms: 121 + 12x + x2 = 225 Solving 121 + 12x + x2 = 225 Solving for variable 'x'. Reorder the terms: 121 + -225 + 12x + x2 = 225 + -225 Combine like terms: 121 + -225 = -104 -104 + 12x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -104 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 12x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 12x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 12x + x2 = 0 + 104 12x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 12x + x2 = 104 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 104 + 36 Reorder the terms: 36 + 12x + x2 = 104 + 36 Combine like terms: 104 + 36 = 140 36 + 12x + x2 = 140 Factor a perfect square on the left side: (x + 6)(x + 6) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + 6) equal to 11.832159566 and -11.832159566.Subproblem 1
x + 6 = 11.832159566 Simplifying x + 6 = 11.832159566 Reorder the terms: 6 + x = 11.832159566 Solving 6 + x = 11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.832159566 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.832159566 + -6 x = 11.832159566 + -6 Combine like terms: 11.832159566 + -6 = 5.832159566 x = 5.832159566 Simplifying x = 5.832159566Subproblem 2
x + 6 = -11.832159566 Simplifying x + 6 = -11.832159566 Reorder the terms: 6 + x = -11.832159566 Solving 6 + x = -11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.832159566 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.832159566 + -6 x = -11.832159566 + -6 Combine like terms: -11.832159566 + -6 = -17.832159566 x = -17.832159566 Simplifying x = -17.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.832159566, -17.832159566}
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