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Simplifying x2 + 12x = -21 Reorder the terms: 12x + x2 = -21 Solving 12x + x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + 12x + x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 12x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 12x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 12x + x2 = 0 + -21 12x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 12x + x2 = -21 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 = -21 + 36 Reorder the terms: 36 + 12x + x2 = -21 + 36 Combine like terms: -21 + 36 = 15 36 + 12x + x2 = 15 Factor a perfect square on the left side: (x + 6)(x + 6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 6) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 6 = 3.872983346 Simplifying x + 6 = 3.872983346 Reorder the terms: 6 + x = 3.872983346 Solving 6 + x = 3.872983346 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 = 3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.872983346 + -6 x = 3.872983346 + -6 Combine like terms: 3.872983346 + -6 = -2.127016654 x = -2.127016654 Simplifying x = -2.127016654Subproblem 2
x + 6 = -3.872983346 Simplifying x + 6 = -3.872983346 Reorder the terms: 6 + x = -3.872983346 Solving 6 + x = -3.872983346 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 = -3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.872983346 + -6 x = -3.872983346 + -6 Combine like terms: -3.872983346 + -6 = -9.872983346 x = -9.872983346 Simplifying x = -9.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.127016654, -9.872983346}
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