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Simplifying x2 + 12x + -876 = 0 Reorder the terms: -876 + 12x + x2 = 0 Solving -876 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '876' to each side of the equation. -876 + 12x + 876 + x2 = 0 + 876 Reorder the terms: -876 + 876 + 12x + x2 = 0 + 876 Combine like terms: -876 + 876 = 0 0 + 12x + x2 = 0 + 876 12x + x2 = 0 + 876 Combine like terms: 0 + 876 = 876 12x + x2 = 876 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 = 876 + 36 Reorder the terms: 36 + 12x + x2 = 876 + 36 Combine like terms: 876 + 36 = 912 36 + 12x + x2 = 912 Factor a perfect square on the left side: (x + 6)(x + 6) = 912 Calculate the square root of the right side: 30.199337741 Break this problem into two subproblems by setting (x + 6) equal to 30.199337741 and -30.199337741.Subproblem 1
x + 6 = 30.199337741 Simplifying x + 6 = 30.199337741 Reorder the terms: 6 + x = 30.199337741 Solving 6 + x = 30.199337741 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 = 30.199337741 + -6 Combine like terms: 6 + -6 = 0 0 + x = 30.199337741 + -6 x = 30.199337741 + -6 Combine like terms: 30.199337741 + -6 = 24.199337741 x = 24.199337741 Simplifying x = 24.199337741Subproblem 2
x + 6 = -30.199337741 Simplifying x + 6 = -30.199337741 Reorder the terms: 6 + x = -30.199337741 Solving 6 + x = -30.199337741 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 = -30.199337741 + -6 Combine like terms: 6 + -6 = 0 0 + x = -30.199337741 + -6 x = -30.199337741 + -6 Combine like terms: -30.199337741 + -6 = -36.199337741 x = -36.199337741 Simplifying x = -36.199337741Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.199337741, -36.199337741}
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