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Simplifying x2 + 12x + -68 = 0 Reorder the terms: -68 + 12x + x2 = 0 Solving -68 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 12x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 12x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 12x + x2 = 0 + 68 12x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 12x + x2 = 68 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 = 68 + 36 Reorder the terms: 36 + 12x + x2 = 68 + 36 Combine like terms: 68 + 36 = 104 36 + 12x + x2 = 104 Factor a perfect square on the left side: (x + 6)(x + 6) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 6) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 6 = 10.198039027 Simplifying x + 6 = 10.198039027 Reorder the terms: 6 + x = 10.198039027 Solving 6 + x = 10.198039027 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 = 10.198039027 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.198039027 + -6 x = 10.198039027 + -6 Combine like terms: 10.198039027 + -6 = 4.198039027 x = 4.198039027 Simplifying x = 4.198039027Subproblem 2
x + 6 = -10.198039027 Simplifying x + 6 = -10.198039027 Reorder the terms: 6 + x = -10.198039027 Solving 6 + x = -10.198039027 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 = -10.198039027 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.198039027 + -6 x = -10.198039027 + -6 Combine like terms: -10.198039027 + -6 = -16.198039027 x = -16.198039027 Simplifying x = -16.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.198039027, -16.198039027}
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