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Simplifying x2 + 66x + -112 = 0 Reorder the terms: -112 + 66x + x2 = 0 Solving -112 + 66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 66x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 66x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 66x + x2 = 0 + 112 66x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 66x + x2 = 112 The x term is 66x. Take half its coefficient (33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. 66x + 1089 + x2 = 112 + 1089 Reorder the terms: 1089 + 66x + x2 = 112 + 1089 Combine like terms: 112 + 1089 = 1201 1089 + 66x + x2 = 1201 Factor a perfect square on the left side: (x + 33)(x + 33) = 1201 Calculate the square root of the right side: 34.655446902 Break this problem into two subproblems by setting (x + 33) equal to 34.655446902 and -34.655446902.Subproblem 1
x + 33 = 34.655446902 Simplifying x + 33 = 34.655446902 Reorder the terms: 33 + x = 34.655446902 Solving 33 + x = 34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = 34.655446902 + -33 Combine like terms: 33 + -33 = 0 0 + x = 34.655446902 + -33 x = 34.655446902 + -33 Combine like terms: 34.655446902 + -33 = 1.655446902 x = 1.655446902 Simplifying x = 1.655446902Subproblem 2
x + 33 = -34.655446902 Simplifying x + 33 = -34.655446902 Reorder the terms: 33 + x = -34.655446902 Solving 33 + x = -34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = -34.655446902 + -33 Combine like terms: 33 + -33 = 0 0 + x = -34.655446902 + -33 x = -34.655446902 + -33 Combine like terms: -34.655446902 + -33 = -67.655446902 x = -67.655446902 Simplifying x = -67.655446902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.655446902, -67.655446902}
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