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Simplifying x2 + 3x + -54 = 11x Reorder the terms: -54 + 3x + x2 = 11x Solving -54 + 3x + x2 = 11x Solving for variable 'x'. Reorder the terms: -54 + 3x + -11x + x2 = 11x + -11x Combine like terms: 3x + -11x = -8x -54 + -8x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -54 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -8x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -8x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -8x + x2 = 0 + 54 -8x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -8x + x2 = 54 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 54 + 16 Reorder the terms: 16 + -8x + x2 = 54 + 16 Combine like terms: 54 + 16 = 70 16 + -8x + x2 = 70 Factor a perfect square on the left side: (x + -4)(x + -4) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -4) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -4 = 8.366600265 Simplifying x + -4 = 8.366600265 Reorder the terms: -4 + x = 8.366600265 Solving -4 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.366600265 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.366600265 + 4 x = 8.366600265 + 4 Combine like terms: 8.366600265 + 4 = 12.366600265 x = 12.366600265 Simplifying x = 12.366600265Subproblem 2
x + -4 = -8.366600265 Simplifying x + -4 = -8.366600265 Reorder the terms: -4 + x = -8.366600265 Solving -4 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.366600265 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.366600265 + 4 x = -8.366600265 + 4 Combine like terms: -8.366600265 + 4 = -4.366600265 x = -4.366600265 Simplifying x = -4.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.366600265, -4.366600265}
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