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Simplifying x2 + -12x + -57 = 0 Reorder the terms: -57 + -12x + x2 = 0 Solving -57 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -12x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + -12x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -12x + x2 = 0 + 57 -12x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 -12x + x2 = 57 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 = 57 + 36 Reorder the terms: 36 + -12x + x2 = 57 + 36 Combine like terms: 57 + 36 = 93 36 + -12x + x2 = 93 Factor a perfect square on the left side: (x + -6)(x + -6) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (x + -6) equal to 9.643650761 and -9.643650761.Subproblem 1
x + -6 = 9.643650761 Simplifying x + -6 = 9.643650761 Reorder the terms: -6 + x = 9.643650761 Solving -6 + x = 9.643650761 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 = 9.643650761 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.643650761 + 6 x = 9.643650761 + 6 Combine like terms: 9.643650761 + 6 = 15.643650761 x = 15.643650761 Simplifying x = 15.643650761Subproblem 2
x + -6 = -9.643650761 Simplifying x + -6 = -9.643650761 Reorder the terms: -6 + x = -9.643650761 Solving -6 + x = -9.643650761 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 = -9.643650761 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.643650761 + 6 x = -9.643650761 + 6 Combine like terms: -9.643650761 + 6 = -3.643650761 x = -3.643650761 Simplifying x = -3.643650761Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.643650761, -3.643650761}
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