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Simplifying x(x) + 12x + 36 = 75 Multiply x * x x2 + 12x + 36 = 75 Reorder the terms: 36 + 12x + x2 = 75 Solving 36 + 12x + x2 = 75 Solving for variable 'x'. Reorder the terms: 36 + -75 + 12x + x2 = 75 + -75 Combine like terms: 36 + -75 = -39 -39 + 12x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -39 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 12x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 12x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 12x + x2 = 0 + 39 12x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 12x + x2 = 39 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 = 39 + 36 Reorder the terms: 36 + 12x + x2 = 39 + 36 Combine like terms: 39 + 36 = 75 36 + 12x + x2 = 75 Factor a perfect square on the left side: (x + 6)(x + 6) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 6) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 6 = 8.660254038 Simplifying x + 6 = 8.660254038 Reorder the terms: 6 + x = 8.660254038 Solving 6 + x = 8.660254038 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 = 8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.660254038 + -6 x = 8.660254038 + -6 Combine like terms: 8.660254038 + -6 = 2.660254038 x = 2.660254038 Simplifying x = 2.660254038Subproblem 2
x + 6 = -8.660254038 Simplifying x + 6 = -8.660254038 Reorder the terms: 6 + x = -8.660254038 Solving 6 + x = -8.660254038 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 = -8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.660254038 + -6 x = -8.660254038 + -6 Combine like terms: -8.660254038 + -6 = -14.660254038 x = -14.660254038 Simplifying x = -14.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.660254038, -14.660254038}
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